subject:( eigenvalue problem)

NSYSU

1. Chang, Hen-wen. The End Game Problem in Solving Algebraic Eigenvalue Problems by Homotopy Continuation Method.

Degree: Master, Applied Mathematics, 2013, NSYSU

URL: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0612113-133039

► The homotopy continuation method is considered to solve polynomial systems. If the number of solutions of the starting system is much more than that of… (more)

Subjects/Keywords: end game problem; eigenvalue problems; homotopy continuation

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APA (6^th Edition):

Chang, H. (2013). The End Game Problem in Solving Algebraic Eigenvalue Problems by Homotopy Continuation Method. (Thesis). NSYSU. Retrieved from http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0612113-133039

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Chang, Hen-wen. “The End Game Problem in Solving Algebraic Eigenvalue Problems by Homotopy Continuation Method.” 2013. Thesis, NSYSU. Accessed April 14, 2021. http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0612113-133039.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Chang, Hen-wen. “The End Game Problem in Solving Algebraic Eigenvalue Problems by Homotopy Continuation Method.” 2013. Web. 14 Apr 2021.

Vancouver:

Chang H. The End Game Problem in Solving Algebraic Eigenvalue Problems by Homotopy Continuation Method. [Internet] [Thesis]. NSYSU; 2013. [cited 2021 Apr 14]. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0612113-133039.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Chang H. The End Game Problem in Solving Algebraic Eigenvalue Problems by Homotopy Continuation Method. [Thesis]. NSYSU; 2013. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0612113-133039

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Wright State University

2. Ali, Ali Hasan. Modifying Some Iterative Methods for Solving Quadratic Eigenvalue Problems.

Degree: MS, Mathematics, 2017, Wright State University

URL: http://rave.ohiolink.edu/etdc/view?acc_num=wright1515029541712239

► In this thesis, we are investigating the solutions λ of a typical quadratic eigenvalue problem (QEP). Indeed, solutions λ of a QEP of the form… (more)

Subjects/Keywords: Mathematics; Applied Mathematics; Quadratic Eigenvalue problem; Matrix Polynomial Problem; Nonlinear Eigenvalue Problem; Newton Iteration; Generalized Eigenvalue Problem; Newton Maehly Method; Newton Maehly Iteration; Newton Correction; QEP; NLEP; NLEVP; MPP; GEP

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APA (6^th Edition):

Ali, A. H. (2017). Modifying Some Iterative Methods for Solving Quadratic Eigenvalue Problems. (Masters Thesis). Wright State University. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=wright1515029541712239

Chicago Manual of Style (16^th Edition):

Ali, Ali Hasan. “Modifying Some Iterative Methods for Solving Quadratic Eigenvalue Problems.” 2017. Masters Thesis, Wright State University. Accessed April 14, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=wright1515029541712239.

MLA Handbook (7^th Edition):

Ali, Ali Hasan. “Modifying Some Iterative Methods for Solving Quadratic Eigenvalue Problems.” 2017. Web. 14 Apr 2021.

Vancouver:

Ali AH. Modifying Some Iterative Methods for Solving Quadratic Eigenvalue Problems. [Internet] [Masters thesis]. Wright State University; 2017. [cited 2021 Apr 14]. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=wright1515029541712239.

Council of Science Editors:

Ali AH. Modifying Some Iterative Methods for Solving Quadratic Eigenvalue Problems. [Masters Thesis]. Wright State University; 2017. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=wright1515029541712239

3. Bohrer, Matheus. Autovalores em variedades Riemannianas completas.

Degree: 2017, Brazil

URL: http://hdl.handle.net/10183/171054

►

O objetivo desta dissertação é estudar o problema de autovalor de Dirichlet para variedades riemannianas completas. Mais precisamente, pretendemos estudar uma cota por baixo para… (more)

Subjects/Keywords: Variedades riemannianas; Autovalores; Dirichlet problem; Yang-type inequality; Eigenvalue problem

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APA (6^th Edition):

Bohrer, M. (2017). Autovalores em variedades Riemannianas completas. (Masters Thesis). Brazil. Retrieved from http://hdl.handle.net/10183/171054

Chicago Manual of Style (16^th Edition):

Bohrer, Matheus. “Autovalores em variedades Riemannianas completas.” 2017. Masters Thesis, Brazil. Accessed April 14, 2021. http://hdl.handle.net/10183/171054.

MLA Handbook (7^th Edition):

Bohrer, Matheus. “Autovalores em variedades Riemannianas completas.” 2017. Web. 14 Apr 2021.

Vancouver:

Bohrer M. Autovalores em variedades Riemannianas completas. [Internet] [Masters thesis]. Brazil; 2017. [cited 2021 Apr 14]. Available from: http://hdl.handle.net/10183/171054.

Council of Science Editors:

Bohrer M. Autovalores em variedades Riemannianas completas. [Masters Thesis]. Brazil; 2017. Available from: http://hdl.handle.net/10183/171054

Universitat Politècnica de València

4. Carreño Sánchez, Amanda María. Integration methods for the time dependent neutron diffusion equation and other approximations of the neutron transport equation .

Degree: 2020, Universitat Politècnica de València

URL: http://hdl.handle.net/10251/144771

► [ES] Uno de los objetivos más importantes en el análisis de la seguridad en el campo de la ingeniería nuclear es el cálculo, rápido y… (more)

▼ [ES] Uno de los objetivos más importantes en el análisis de la seguridad en el campo de la ingeniería nuclear es el cálculo, rápido y preciso, de la evolución de la potencia dentro del núcleo del reactor. La distribución de los neutrones se puede describir a través de la ecuación de transporte de Boltzmann. La solución de esta ecuación no puede obtenerse de manera sencilla para reactores realistas, y es por ello que se tienen que considerar aproximaciones numéricas. En primer lugar, esta tesis se centra en obtener la solución para varios problemas estáticos asociados con la ecuación de difusión neutrónica: los modos lambda, los modos gamma y los modos alpha. Para la discretización espacial se ha utilizado un método de elementos finitos de alto orden. Diversas características de cada problema espectral se analizan y se comparan en diferentes reactores. Después, se investigan varios métodos de cálculo para problemas de autovalores y estrategias para calcular los problemas algebraicos obtenidos a partir de la discretización espacial. La mayoría de los trabajos destinados a la resolución de la ecuación de difusión neutrónica están diseñados para la aproximación de dos grupos de energía, sin considerar dispersión de neutrones del grupo térmico al grupo rápido. La principal ventaja de la metodología que se propone es que no depende de la geometría del reactor, del tipo de problema de autovalores ni del número de grupos de energía del problema. Tras esto, se obtiene la solución de las ecuaciones estacionarias de armónicos esféricos. La implementación de estas ecuaciones tiene dos principales diferencias respecto a la ecuación de difusión neutrónica. Primero, la discretización espacial se realiza a nivel de pin. Por tanto, se estudian diferentes tipos de mallas. Segundo, el número de grupos de energía es, generalmente, mayor que dos. De este modo, se desarrollan estrategias a bloques para optimizar el cálculo de los problemas algebraicos asociados. Finalmente, se implementa un método modal actualizado para integrar la ecuación de difusión neutrónica dependiente del tiempo. Se presentan y comparan los métodos modales basados en desarrollos en función de los diferentes modos espaciales para varios tipos de transitorios. Además, también se desarrolla un control de paso de tiempo adaptativo, que evita la actualización de los modos de una manera fija y adapta el paso de tiempo en función de varias estimaciones del error. Advisors/Committee Members: Ginestar Peiro, Damián (advisor), Verdú Martín, Gumersindo Jesús (advisor), Vidal Ferràndiz, Antoni (advisor).

Subjects/Keywords: Eigenvalue problem solvers; Neutron transport equation; Finite element method; Nuclear engineering

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Carreño Sánchez, A. M. (2020). Integration methods for the time dependent neutron diffusion equation and other approximations of the neutron transport equation . (Doctoral Dissertation). Universitat Politècnica de València. Retrieved from http://hdl.handle.net/10251/144771

Chicago Manual of Style (16^th Edition):

Carreño Sánchez, Amanda María. “Integration methods for the time dependent neutron diffusion equation and other approximations of the neutron transport equation .” 2020. Doctoral Dissertation, Universitat Politècnica de València. Accessed April 14, 2021. http://hdl.handle.net/10251/144771.

MLA Handbook (7^th Edition):

Carreño Sánchez, Amanda María. “Integration methods for the time dependent neutron diffusion equation and other approximations of the neutron transport equation .” 2020. Web. 14 Apr 2021.

Vancouver:

Carreño Sánchez AM. Integration methods for the time dependent neutron diffusion equation and other approximations of the neutron transport equation . [Internet] [Doctoral dissertation]. Universitat Politècnica de València; 2020. [cited 2021 Apr 14]. Available from: http://hdl.handle.net/10251/144771.

Council of Science Editors:

Carreño Sánchez AM. Integration methods for the time dependent neutron diffusion equation and other approximations of the neutron transport equation . [Doctoral Dissertation]. Universitat Politècnica de València; 2020. Available from: http://hdl.handle.net/10251/144771

University of Minnesota

5. Kalantzis, Vasileios. Domain decomposition algorithms for the solution of sparse symmetric generalized eigenvalue problems.

Degree: PhD, Computer Science, 2018, University of Minnesota

URL: http://hdl.handle.net/11299/201170

► This dissertation focuses on the design, implementation, and evaluation of domain decomposition techniques for the solution of large and sparse algebraic symmetric generalized eigenvalue problems.… (more)

▼ This dissertation focuses on the design, implementation, and evaluation of domain decomposition techniques for the solution of large and sparse algebraic symmetric generalized eigenvalue problems. Domain decomposition techniques begin by partitioning the global (discretized) domain into a number of subdomains. The solution of the algebraic eigenvalue problem is then decoupled into two separate subproblems: (1) one defined locally in the interior of each subdomain, and (2) one defined on the interface region connecting neighboring subdomains. As soon as the part of the solution associated with the interface region is computed, the part of the solution associated with the interior variables in each subdomain can be computed locally and independently of the rest of the subdomains. The domain decomposition techniques proposed in this dissertation can be classified into two categories: (1) filtering techniques, and (2) root-finding techniques. Filtering techniques are projection methods applied to a transformation of the original matrix pencil chosen so that, ideally, the eigenvalues of interest are mapped to the only nonzero eigenvalues in the transformed pencil. This dissertation combines domain decomposition with filtering approaches and demonstrates how this class of hybrid algorithms can outperform current state-of-the-art filtering techniques. Apart being well-suited for execution on distributed memory systems, an immediate advantage of such hybrid techniques is that any orthogonalization necessary needs to be performed only to vectors whose length is equal to the number of interface variables. Moreover, we show that if the filter is applied only to that portion of the pencil associated with the interface variables, it is possible to even achieve convergence within a number of steps that is smaller than the number of eigenvalues located inside the interval of interest. In contrast, any projection method applied to a transformation of the original matrix pencil must perform a number of steps that is at least equal to the number of eigenvalues located inside the interval of interest. Implementation aspects of the proposed numerical schemes on many-core/multi-core computer systems and experiments on serial/distributed computing environments are also discussed. Root-finding techniques convert the interface eigenvalue problem into one of computing roots of scalar functions, i.e., the eigenvalues of the original eigenvalue problem are roots of a carefully chosen scalar function. This allows the use of existing fast iterative root-finding schemes, e.g. Newton's method, for the solution of symmetric generalized eigenvalue problems. Root-finding techniques can be especially useful when only a few eigenvalues and associated eigenvectors are sought. The numerical schemes proposed in this part of the present dissertation are compared against other single-vector eigenvalue solvers such as the Rayleigh Quotient Iteration and Residual Inverse Iteration. Numerous theoretical details and practical…

Subjects/Keywords: Domain decomposition; Eigenvalues; Schur complement; Sparse matrices; Symmetric generalized eigenvalue problem

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APA (6^th Edition):

Kalantzis, V. (2018). Domain decomposition algorithms for the solution of sparse symmetric generalized eigenvalue problems. (Doctoral Dissertation). University of Minnesota. Retrieved from http://hdl.handle.net/11299/201170

Chicago Manual of Style (16^th Edition):

Kalantzis, Vasileios. “Domain decomposition algorithms for the solution of sparse symmetric generalized eigenvalue problems.” 2018. Doctoral Dissertation, University of Minnesota. Accessed April 14, 2021. http://hdl.handle.net/11299/201170.

MLA Handbook (7^th Edition):

Kalantzis, Vasileios. “Domain decomposition algorithms for the solution of sparse symmetric generalized eigenvalue problems.” 2018. Web. 14 Apr 2021.

Vancouver:

Kalantzis V. Domain decomposition algorithms for the solution of sparse symmetric generalized eigenvalue problems. [Internet] [Doctoral dissertation]. University of Minnesota; 2018. [cited 2021 Apr 14]. Available from: http://hdl.handle.net/11299/201170.

Council of Science Editors:

Kalantzis V. Domain decomposition algorithms for the solution of sparse symmetric generalized eigenvalue problems. [Doctoral Dissertation]. University of Minnesota; 2018. Available from: http://hdl.handle.net/11299/201170

Louisiana State University

6. Ramachandran, Prashanth. Stability problems in constrained pendulum systems and time-delayed systems.

Degree: PhD, Mechanical Engineering, 2012, Louisiana State University

URL: etd-07132012-041706 ; https://digitalcommons.lsu.edu/gradschool_dissertations/581

► In this dissertation, we study the boundary of stability of a class of linear mechanical systems as a function of a parameter. We consider two… (more)

▼ In this dissertation, we study the boundary of stability of a class of linear mechanical systems as a function of a parameter. We consider two different systems under this class: a constrained double pendulum connected by a rigid rod and a state-feedback-controlled mechanical system with time delay. In the first system, the destabilizing parameter is the distance between the supports of the two pendulums. In the second system, the destabilizing parameter is the time delay. In the constrained double pendulum system, linear perturbation analysis is used to determine the natural frequency of the system. Our analysis reveals a zone of instability in what seemingly is an inherently stable configuration. This paradoxical behavior, which is not mentioned in the literature until now, is explained and a simple experiment confirms the instability predicted by the analysis. The approach is extended to a chain of pendulums consisting of n masses and n+1 links, which is a lumped parameter model for small vibrations of a catenary. Our work confirms the existence of asymmetric stable equilibrium configurations for a symmetric system. The problem of determining the critical distance for instability between two supporting points of a catenary has potential application in the design of novel mechanical switches, sensors, and valves. In the second part of the dissertation, we consider a linear mechanical system where a time delay exists in the linear state feedback control input. We seek a closed-form solution for the problem of determining the critical time delay for instability of the closed-loop system. Such a closed-form solution, which to the best of our knowledge is inexistent in the literature, offers an exact value for the critical time delay whereas a numerical solution is only approximate. We show that in the single-input/multi-output (SIMO) case of the class of systems under consideration, the problem may be reduced by using singular value decomposition to that of finding the roots of a certain polynomial. The obtained closed-form solution accurately predicts the smallest time delay that would render the SIMO system unstable when the control gain matrices have a unit rank. This technique however cannot be extended to the multi-input/multi-output case. Two numerical methods are therefore developed to solve this case. One method involves Newton’s iterations and the other method involves bisection for multiple functions.

Subjects/Keywords: Stability; Double Pendulum; Time-Delay; Transcendental Eigenvalue Problem

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APA (6^th Edition):

Ramachandran, P. (2012). Stability problems in constrained pendulum systems and time-delayed systems. (Doctoral Dissertation). Louisiana State University. Retrieved from etd-07132012-041706 ; https://digitalcommons.lsu.edu/gradschool_dissertations/581

Chicago Manual of Style (16^th Edition):

Ramachandran, Prashanth. “Stability problems in constrained pendulum systems and time-delayed systems.” 2012. Doctoral Dissertation, Louisiana State University. Accessed April 14, 2021. etd-07132012-041706 ; https://digitalcommons.lsu.edu/gradschool_dissertations/581.

MLA Handbook (7^th Edition):

Ramachandran, Prashanth. “Stability problems in constrained pendulum systems and time-delayed systems.” 2012. Web. 14 Apr 2021.

Vancouver:

Ramachandran P. Stability problems in constrained pendulum systems and time-delayed systems. [Internet] [Doctoral dissertation]. Louisiana State University; 2012. [cited 2021 Apr 14]. Available from: etd-07132012-041706 ; https://digitalcommons.lsu.edu/gradschool_dissertations/581.

Council of Science Editors:

Ramachandran P. Stability problems in constrained pendulum systems and time-delayed systems. [Doctoral Dissertation]. Louisiana State University; 2012. Available from: etd-07132012-041706 ; https://digitalcommons.lsu.edu/gradschool_dissertations/581

University of Manchester

7. Zemaityte, Mante. Theory and Algorithms for Linear Eigenvalue Problems.

Degree: 2020, University of Manchester

URL: http://www.manchester.ac.uk/escholar/uk-ac-man-scw:323865

► In the first part of this thesis, methods for the partial solution of generalized eigenvalue problems arising from structural dynamics are studied. A natural choice… (more)

▼ In the first part of this thesis, methods for the partial solution of generalized eigenvalue problems arising from structural dynamics are studied. A natural choice for partially solving the generalized eigenvalue problem (GEP) is the Lanczos iteration, or the shift-and-invert Lanczos (SIL) algorithm if a large number of eigenpairs is required. When the external loading of the associated structural dynamics problem is specific to that of earthquake engineering, the contribution of an eigenvector of a generalized eigenvalue problem can be quantified by a simple expression. Based on this property, a novel shifting strategy for the SIL algorithm which arises from the theory of orthogonal polynomials is presented. We discuss the Lanczos algorithm and its variant suited for the partial solution of the GEP arising from structural dynamics, followed by the shift-and-invert Lanczos algorithm. Various theoretical aspects and numerical issues of these algorithms are examined and addressed. The Ritz vector and the Lanczos vector methods are also introduced. These methods use vectors other than eigenvectors for the solution of structural dynamics problems. The Ritz vector method is widely used by engineers and is often implemented in engineering software. Orthogonal polynomials and the theory required to devise a new shifting strategy for the SIL algorithm are then introduced. With a specific choice of the starting vector for the Lanczos process it becomes possible to identify the intervals of the spectrum of the associated GEP in which the eigenvalues corresponding to the eigenvectors of interest lie. The shifts for the SIL algorithm are then chosen in the middle of these intervals, and a stopping criterion is provided. The algorithm is termed MASIL. The numerical experiments are performed on real engineering problems with our implementations of SIL, MASIL, Ritz vector, and Lanczos vector methods. While providing a comparable approximation to the solution of the structural dynamics problem, the MASIL approach computes up to 70% fewer eigenvectors and requires fewer shifts, on average, when compared with the standard shifting strategy used for this problem. The Ritz and Lanczos vector methods often provide an accurate approximation to the solution of the structural dynamics problem, but we show that there are cases where these methods do not provide a satisfactory approximation. In the second part of this thesis we explore max-plus algebra. It has been recently observed that an order of magnitude approximations to the absolute values of the eigenvalues of linear and polynomial eigenvalue problems can be obtained by the use of max-plus algebra, when the underlying matrices are unstructured and have large variations between the magnitudes of their entries. We extend the existing algorithms to return only some of the eigenvalues of the standard and generalized max-plus eigenvalue problems, and provide a result which allows for an estimation of the number of eigenvalues in modulus in a given interval. We then present numerical… Advisors/Committee Members: HIGHAM, NICHOLAS NJ, Tisseur, Francoise, Higham, Nicholas.

Subjects/Keywords: shift-and-invert Lanczos algorithm; symmetric generalized eigenvalue problem; shifting strategy; structural analysis; orthogonal polynomials; max-plus eigenvalue problems

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Zemaityte, M. (2020). Theory and Algorithms for Linear Eigenvalue Problems. (Doctoral Dissertation). University of Manchester. Retrieved from http://www.manchester.ac.uk/escholar/uk-ac-man-scw:323865

Chicago Manual of Style (16^th Edition):

Zemaityte, Mante. “Theory and Algorithms for Linear Eigenvalue Problems.” 2020. Doctoral Dissertation, University of Manchester. Accessed April 14, 2021. http://www.manchester.ac.uk/escholar/uk-ac-man-scw:323865.

MLA Handbook (7^th Edition):

Zemaityte, Mante. “Theory and Algorithms for Linear Eigenvalue Problems.” 2020. Web. 14 Apr 2021.

Vancouver:

Zemaityte M. Theory and Algorithms for Linear Eigenvalue Problems. [Internet] [Doctoral dissertation]. University of Manchester; 2020. [cited 2021 Apr 14]. Available from: http://www.manchester.ac.uk/escholar/uk-ac-man-scw:323865.

Council of Science Editors:

Zemaityte M. Theory and Algorithms for Linear Eigenvalue Problems. [Doctoral Dissertation]. University of Manchester; 2020. Available from: http://www.manchester.ac.uk/escholar/uk-ac-man-scw:323865

University of Manchester

8. Zemaityte, Mante. Theory and algorithms for linear eigenvalue problems.

Degree: PhD, 2020, University of Manchester

URL: https://www.research.manchester.ac.uk/portal/en/theses/theory-and-algorithms-for-linear-eigenvalue-problems(d363b322-5b7f-420c-930a-91dfad9a9c0f).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.799528

► In the first part of this thesis, methods for the partial solution of generalized eigenvalue problems arising from structural dynamics are studied. A natural choice… (more)

▼ In the first part of this thesis, methods for the partial solution of generalized eigenvalue problems arising from structural dynamics are studied. A natural choice for partially solving the generalized eigenvalue problem (GEP) is the Lanczos iteration, or the shift-and-invert Lanczos (SIL) algorithm if a large number of eigenpairs is required. When the external loading of the associated structural dynamics problem is specific to that of earthquake engineering, the contribution of an eigenvector of a generalized eigenvalue problem can be quantified by a simple expression. Based on this property, a novel shifting strategy for the SIL algorithm which arises from the theory of orthogonal polynomials is presented. We discuss the Lanczos algorithm and its variant suited for the partial solution of the GEP arising from structural dynamics, followed by the shift-and-invert Lanczos algorithm. Various theoretical aspects and numerical issues of these algorithms are examined and addressed. The Ritz vector and the Lanczos vector methods are also introduced. These methods use vectors other than eigenvectors for the solution of structural dynamics problems. The Ritz vector method is widely used by engineers and is often implemented in engineering software. Orthogonal polynomials and the theory required to devise a new shifting strategy for the SIL algorithm are then introduced. With a specific choice of the starting vector for the Lanczos process it becomes possible to identify the intervals of the spectrum of the associated GEP in which the eigenvalues corresponding to the eigenvectors of interest lie. The shifts for the SIL algorithm are then chosen in the middle of these intervals, and a stopping criterion is provided. The algorithm is termed MASIL. The numerical experiments are performed on real engineering problems with our implementations of SIL, MASIL, Ritz vector, and Lanczos vector methods. While providing a comparable approximation to the solution of the structural dynamics problem, the MASIL approach computes up to 70% fewer eigenvectors and requires fewer shifts, on average, when compared with the standard shifting strategy used for this problem. The Ritz and Lanczos vector methods often provide an accurate approximation to the solution of the structural dynamics problem, but we show that there are cases where these methods do not provide a satisfactory approximation. In the second part of this thesis we explore max-plus algebra. It has been recently observed that an order of magnitude approximations to the absolute values of the eigenvalues of linear and polynomial eigenvalue problems can be obtained by the use of max-plus algebra, when the underlying matrices are unstructured and have large variations between the magnitudes of their entries. We extend the existing algorithms to return only some of the eigenvalues of the standard and generalized max-plus eigenvalue problems, and provide a result which allows for an estimation of the number of eigenvalues in modulus in a given interval. We then present numerical…

Subjects/Keywords: max-plus eigenvalue problems; orthogonal polynomials; structural analysis; symmetric generalized eigenvalue problem; shift-and-invert Lanczos algorithm; shifting strategy

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APA (6^th Edition):

Zemaityte, M. (2020). Theory and algorithms for linear eigenvalue problems. (Doctoral Dissertation). University of Manchester. Retrieved from https://www.research.manchester.ac.uk/portal/en/theses/theory-and-algorithms-for-linear-eigenvalue-problems(d363b322-5b7f-420c-930a-91dfad9a9c0f).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.799528

Chicago Manual of Style (16^th Edition):

Zemaityte, Mante. “Theory and algorithms for linear eigenvalue problems.” 2020. Doctoral Dissertation, University of Manchester. Accessed April 14, 2021. https://www.research.manchester.ac.uk/portal/en/theses/theory-and-algorithms-for-linear-eigenvalue-problems(d363b322-5b7f-420c-930a-91dfad9a9c0f).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.799528.

MLA Handbook (7^th Edition):

Zemaityte, Mante. “Theory and algorithms for linear eigenvalue problems.” 2020. Web. 14 Apr 2021.

Vancouver:

Zemaityte M. Theory and algorithms for linear eigenvalue problems. [Internet] [Doctoral dissertation]. University of Manchester; 2020. [cited 2021 Apr 14]. Available from: https://www.research.manchester.ac.uk/portal/en/theses/theory-and-algorithms-for-linear-eigenvalue-problems(d363b322-5b7f-420c-930a-91dfad9a9c0f).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.799528.

Council of Science Editors:

Zemaityte M. Theory and algorithms for linear eigenvalue problems. [Doctoral Dissertation]. University of Manchester; 2020. Available from: https://www.research.manchester.ac.uk/portal/en/theses/theory-and-algorithms-for-linear-eigenvalue-problems(d363b322-5b7f-420c-930a-91dfad9a9c0f).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.799528

9. Pallikarakis, Nikolaos. Το αντίστροφο φασματικό πρόβλημα της εύρεσης του δείκτη διάθλασης για το εσωτερικό πρόβλημα διαπερατότητας.

Degree: 2017, National Technical University of Athens (NTUA); Εθνικό Μετσόβιο Πολυτεχνείο (ΕΜΠ)

URL: http://hdl.handle.net/10442/hedi/40578

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The main object of this thesis is the investigation of the inverse transmission eigenvalue problem, that is the determination of the refractive index of an… (more)

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The main object of this thesis is the investigation of the inverse transmission eigenvalue problem, that is the determination of the refractive index of an inhomogeneous medium from transmission eigenvalues. Using some known results for the case where the refractive index is a radially symmetric and C2 function, we introduce the corresponding interior transmission eigenvalue problem for a discontinuous refractive index. We examine the asymptotic properties of the eigenfunctions for large values of the spectral parameter, and investigate their dependence upon the discontinuity. We prove that the discontinuous refractive index is uniquely determined from the knowledge of all transmission eigenvalues, with no restrictions on the position of the discontinuity.Furthermore, we propose a numerical method to compute transmission eigenvalues.We adopt a Galerkin-type method which is based on the variational formulation of the problem. Using a proper operator representation we show convergence of the method.We define the inverse transmission problem and show that numerically the problem can be considered as an inverse quadratic eigenvalue problem. We investigate the case of a spherically symmetric and piecewise constant refractive index and show that a small number of eigenvalues is sufficient for the reconstructions. We also introduce a computational method based on a Newton-type algorithm for reconstructions of arbitrary piecewise constant index from transmission eigenvalues. We illustrate our method with several examples.Particularly, our aim is to study the properties of the discontinuous transmission eigenvalue problem and examine how the presence of a discontinuity affect the inverse problem. Our work has been motivated by the inverse problem of recovering material properties of a medium with layers with applications in non-destructive testing and target identification.

Σκοπός της παρούσας διδακτορικής διατριβής είναι η μελέτη του αντίστροφου εσωτερικού προβλήματος διαπερατότητας (inverse transmission eigenvalue problem), δηλαδή του προσδιορισμού του δείκτη διάθλασης ενός μη ομογενούς μέσου από τις ιδιοτιμές διαπερατότητας (transmission eiegenvalues). Βασιζόμενοι σε γνωστά αποτελέσματα για την περίπτωση όπου ο δείκτης διάθλασης είναι σφαιρικά συμμετρικός και C2 συνάρτηση, διατυπώνουμε το αντίστροφο φασματικό πρόβλημα για τον δείκτη διάθλασης με ασυνέχειες. Διερευνάμε την ασυμπτωτική συμπεριφορά των ιδιοσυναρτήσεων για μεγάλες τιμές της φασματικής παραμέτρου, και μελετάμε την εξάρτησή τους από την ασυνέχεια. Αποδεικνύουμε ότι ο ασυνεχής δείκτης μπορεί να προσδιοριστεί μοναδικά από τη γνώση όλων των ιδιοτιμών διαπερατότητας, χωρίς περιορισμούς στη θέση της ασυνέχειας.Στη συνέχεια, προτείνουμε μία αριθμητική μέθοδο για τον υπολογισμό των ιδιοτιμών διαπερατότητας. Υιοθετούμε μία μέθοδο τύπου Galerkin η οποία βασίζεται στη μεταβολική διατύπωση του προβλήματος. Με την κατάλληλη αναπαράσταση του προβλήματος ως ένα πρόβλημα τελεστών αποδεικνύουμε τη σύγκλιση της μεθόδου. Έπειτα, ορίζουμε το αντίστροφο πρόβλημα διαπερατότητας…

Subjects/Keywords: Εσωτερικό πρόβλημα διαπερατότητας; Ιδιοτιμές διαπερατότητας; Αντίστροφο πρόβλημα διαπερατότητας; Ασυνεχές αντίστροφο πρόβλημα ιδιοτιμών; Αντίστροφο φασματικό πρόβλημα; Τετραγωνικό πρόβλημα ιδιοτιμών; Κατά τμήματα σταθερός δείκτης διάθλασης; Interior transmission problem; Transmission eigenalues; Inverse transmission eigenvalue problem; Discontinuous inverse eigenvalue problem; Inverse spectral problem; Quadratic eigenvalue problem; Piecewise constant refractive index

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APA (6^th Edition):

Pallikarakis, N. (2017). Το αντίστροφο φασματικό πρόβλημα της εύρεσης του δείκτη διάθλασης για το εσωτερικό πρόβλημα διαπερατότητας. (Thesis). National Technical University of Athens (NTUA); Εθνικό Μετσόβιο Πολυτεχνείο (ΕΜΠ). Retrieved from http://hdl.handle.net/10442/hedi/40578

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Pallikarakis, Nikolaos. “Το αντίστροφο φασματικό πρόβλημα της εύρεσης του δείκτη διάθλασης για το εσωτερικό πρόβλημα διαπερατότητας.” 2017. Thesis, National Technical University of Athens (NTUA); Εθνικό Μετσόβιο Πολυτεχνείο (ΕΜΠ). Accessed April 14, 2021. http://hdl.handle.net/10442/hedi/40578.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Pallikarakis, Nikolaos. “Το αντίστροφο φασματικό πρόβλημα της εύρεσης του δείκτη διάθλασης για το εσωτερικό πρόβλημα διαπερατότητας.” 2017. Web. 14 Apr 2021.

Vancouver:

Pallikarakis N. Το αντίστροφο φασματικό πρόβλημα της εύρεσης του δείκτη διάθλασης για το εσωτερικό πρόβλημα διαπερατότητας. [Internet] [Thesis]. National Technical University of Athens (NTUA); Εθνικό Μετσόβιο Πολυτεχνείο (ΕΜΠ); 2017. [cited 2021 Apr 14]. Available from: http://hdl.handle.net/10442/hedi/40578.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Pallikarakis N. Το αντίστροφο φασματικό πρόβλημα της εύρεσης του δείκτη διάθλασης για το εσωτερικό πρόβλημα διαπερατότητας. [Thesis]. National Technical University of Athens (NTUA); Εθνικό Μετσόβιο Πολυτεχνείο (ΕΜΠ); 2017. Available from: http://hdl.handle.net/10442/hedi/40578

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

NSYSU

10. LEE, YU-HAO. The theory of transformation operators and its application in inverse spectral problems.

Degree: Master, Applied Mathematics, 2005, NSYSU

URL: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0704105-182611

► The inverse spectral problem is the problem of understanding the potential function of the Sturm-Liouville operator from the set of eigenvalues plus some additional spectral… (more)

Subjects/Keywords: eigenvalue; Transformation operator; spectral problem; eigenvector

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APA (6^th Edition):

LEE, Y. (2005). The theory of transformation operators and its application in inverse spectral problems. (Thesis). NSYSU. Retrieved from http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0704105-182611

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

LEE, YU-HAO. “The theory of transformation operators and its application in inverse spectral problems.” 2005. Thesis, NSYSU. Accessed April 14, 2021. http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0704105-182611.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

LEE, YU-HAO. “The theory of transformation operators and its application in inverse spectral problems.” 2005. Web. 14 Apr 2021.

Vancouver:

LEE Y. The theory of transformation operators and its application in inverse spectral problems. [Internet] [Thesis]. NSYSU; 2005. [cited 2021 Apr 14]. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0704105-182611.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

LEE Y. The theory of transformation operators and its application in inverse spectral problems. [Thesis]. NSYSU; 2005. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0704105-182611

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Bath

11. Scheben, Fynn. Iterative methods for criticality computations in neutron transport theory.

Degree: PhD, 2011, University of Bath

URL: https://researchportal.bath.ac.uk/en/studentthesis/iterative-methods-for-criticality-computations-in-neutron-transport-theory(286d7964-202f-43d2-b41c-4a3fb3732b52).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.545319

► This thesis studies the so-called “criticality problem”, an important generalised eigenvalue problem arising in neutron transport theory. The smallest positive real eigenvalue of the problem… (more)

▼ This thesis studies the so-called “criticality problem”, an important generalised eigenvalue problem arising in neutron transport theory. The smallest positive real eigenvalue of the problem contains valuable information about the status of the fission chain reaction in the nuclear reactor (i.e. the criticality of the reactor), and thus plays an important role in the design and safety of nuclear power stations. Because of the practical importance, efficient numerical methods to solve the criticality problem are needed, and these are the focus of this thesis. In the theory we consider the time-independent neutron transport equation in the monoenergetic homogeneous case with isotropic scattering and vacuum boundary conditions. This is an unsymmetric integro-differential equation in 5 independent variables, modelling transport, scattering, and fission, where the dependent variable is the neutron angular flux. We show that, before discretisation, the nonsymmetric eigenproblem for the angular flux is equivalent to a related eigenproblem for the scalar flux, involving a symmetric positive definite weakly singular integral operator(in space only). Furthermore, we prove the existence of a simple smallest positive real eigenvalue with a corresponding eigenfunction that is strictly positive in the interior of the reactor. We discuss approaches to discretise the problem and present discretisations that preserve the underlying symmetry in the finite dimensional form. The thesis then describes methods for computing the criticality in nuclear reactors, i.e. the smallest positive real eigenvalue, which are applicable for quite general geometries and physics. In engineering practice the criticality problem is often solved iteratively, using some variant of the inverse power method. Because of the high dimension, matrix representations for the operators are often not available and the inner solves needed for the eigenvalue iteration are implemented by matrix-free inneriterations. This leads to inexact iterative methods for criticality computations, for which there appears to be no rigorous convergence theory. The fact that, under appropriate assumptions, the integro-differential eigenvalue problem possesses an underlying symmetry (in a space of reduced dimension) allows us to perform a systematic convergence analysis for inexact inverse iteration and related methods. In particular, this theory provides rather precise criteria on how accurate the inner solves need to be in order for the whole iterative method to converge. The theory is illustrated with numerical examples on several test problems of physical relevance, using GMRES as the inner solver. We also illustrate the use of Monte Carlo methods for the solution of neutron transport source problems as well as for the criticality problem. Links between the steps in the Monte Carlo process and the underlying mathematics are emphasised and numerical examples are given. Finally, we introduce an iterative scheme (the so-called “method of perturbation”) that is based on computing the…

Subjects/Keywords: 518; linear Boltzmann equation; criticality; neutron transport; inverse iteration; inexact solves; iterative methods; eigenvalue problem

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APA (6^th Edition):

Scheben, F. (2011). Iterative methods for criticality computations in neutron transport theory. (Doctoral Dissertation). University of Bath. Retrieved from https://researchportal.bath.ac.uk/en/studentthesis/iterative-methods-for-criticality-computations-in-neutron-transport-theory(286d7964-202f-43d2-b41c-4a3fb3732b52).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.545319

Chicago Manual of Style (16^th Edition):

Scheben, Fynn. “Iterative methods for criticality computations in neutron transport theory.” 2011. Doctoral Dissertation, University of Bath. Accessed April 14, 2021. https://researchportal.bath.ac.uk/en/studentthesis/iterative-methods-for-criticality-computations-in-neutron-transport-theory(286d7964-202f-43d2-b41c-4a3fb3732b52).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.545319.

MLA Handbook (7^th Edition):

Scheben, Fynn. “Iterative methods for criticality computations in neutron transport theory.” 2011. Web. 14 Apr 2021.

Vancouver:

Scheben F. Iterative methods for criticality computations in neutron transport theory. [Internet] [Doctoral dissertation]. University of Bath; 2011. [cited 2021 Apr 14]. Available from: https://researchportal.bath.ac.uk/en/studentthesis/iterative-methods-for-criticality-computations-in-neutron-transport-theory(286d7964-202f-43d2-b41c-4a3fb3732b52).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.545319.

Council of Science Editors:

Scheben F. Iterative methods for criticality computations in neutron transport theory. [Doctoral Dissertation]. University of Bath; 2011. Available from: https://researchportal.bath.ac.uk/en/studentthesis/iterative-methods-for-criticality-computations-in-neutron-transport-theory(286d7964-202f-43d2-b41c-4a3fb3732b52).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.545319

University of Central Florida

12. Adams, Christine. Can One Hear...? An Exploration Into Inverse Eigenvalue Problems Related To Musical Instruments.

Degree: 2013, University of Central Florida

URL: https://stars.library.ucf.edu/etd/2506

► The central theme of this thesis deals with problems related to the question, “Can one hear the shape of a drum?” first posed formally by… (more)

Subjects/Keywords: Inverse eigenvalue problem; music; drum; Mathematics; Dissertations, Academic – Sciences, Sciences – Dissertations, Academic

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APA (6^th Edition):

Adams, C. (2013). Can One Hear...? An Exploration Into Inverse Eigenvalue Problems Related To Musical Instruments. (Masters Thesis). University of Central Florida. Retrieved from https://stars.library.ucf.edu/etd/2506

Chicago Manual of Style (16^th Edition):

Adams, Christine. “Can One Hear...? An Exploration Into Inverse Eigenvalue Problems Related To Musical Instruments.” 2013. Masters Thesis, University of Central Florida. Accessed April 14, 2021. https://stars.library.ucf.edu/etd/2506.

MLA Handbook (7^th Edition):

Adams, Christine. “Can One Hear...? An Exploration Into Inverse Eigenvalue Problems Related To Musical Instruments.” 2013. Web. 14 Apr 2021.

Vancouver:

Adams C. Can One Hear...? An Exploration Into Inverse Eigenvalue Problems Related To Musical Instruments. [Internet] [Masters thesis]. University of Central Florida; 2013. [cited 2021 Apr 14]. Available from: https://stars.library.ucf.edu/etd/2506.

Council of Science Editors:

Adams C. Can One Hear...? An Exploration Into Inverse Eigenvalue Problems Related To Musical Instruments. [Masters Thesis]. University of Central Florida; 2013. Available from: https://stars.library.ucf.edu/etd/2506

Virginia Tech

13. Just, Frederick A. Damage Detection Based on the Geometric Interpretation of the Eigenvalue Problem.

Degree: PhD, Engineering Science and Mechanics, 1997, Virginia Tech

URL: http://hdl.handle.net/10919/29555

► A method that can be used to detect damage in structures is developed. This method is based on the convexity of the geometric interpretation of… (more)

Subjects/Keywords: Eigenvalue Problem; Convex Set; Damage Detection

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APA (6^th Edition):

Just, F. A. (1997). Damage Detection Based on the Geometric Interpretation of the Eigenvalue Problem. (Doctoral Dissertation). Virginia Tech. Retrieved from http://hdl.handle.net/10919/29555

Chicago Manual of Style (16^th Edition):

Just, Frederick A. “Damage Detection Based on the Geometric Interpretation of the Eigenvalue Problem.” 1997. Doctoral Dissertation, Virginia Tech. Accessed April 14, 2021. http://hdl.handle.net/10919/29555.

MLA Handbook (7^th Edition):

Just, Frederick A. “Damage Detection Based on the Geometric Interpretation of the Eigenvalue Problem.” 1997. Web. 14 Apr 2021.

Vancouver:

Just FA. Damage Detection Based on the Geometric Interpretation of the Eigenvalue Problem. [Internet] [Doctoral dissertation]. Virginia Tech; 1997. [cited 2021 Apr 14]. Available from: http://hdl.handle.net/10919/29555.

Council of Science Editors:

Just FA. Damage Detection Based on the Geometric Interpretation of the Eigenvalue Problem. [Doctoral Dissertation]. Virginia Tech; 1997. Available from: http://hdl.handle.net/10919/29555

Kansas State University

14. Xu, Leidong. Acceleration of the power and related methods with dynamic mode decomposition.

Degree: MS, Department of Mechanical and Nuclear Engineering, 2019, Kansas State University

URL: http://hdl.handle.net/2097/40267

► An algorithm based on dynamic mode decomposition (DMD) is presented for acceleration of the power method (PM) and fattened power method (FPM) that takes advantage… (more)

Subjects/Keywords: Power method; Dynamic Mode Decomposition; Acceleration; Nuclear Engineering; Numerical Simulation; Eigenvalue Problem

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APA (6^th Edition):

Xu, L. (2019). Acceleration of the power and related methods with dynamic mode decomposition. (Masters Thesis). Kansas State University. Retrieved from http://hdl.handle.net/2097/40267

Chicago Manual of Style (16^th Edition):

Xu, Leidong. “Acceleration of the power and related methods with dynamic mode decomposition.” 2019. Masters Thesis, Kansas State University. Accessed April 14, 2021. http://hdl.handle.net/2097/40267.

MLA Handbook (7^th Edition):

Xu, Leidong. “Acceleration of the power and related methods with dynamic mode decomposition.” 2019. Web. 14 Apr 2021.

Vancouver:

Xu L. Acceleration of the power and related methods with dynamic mode decomposition. [Internet] [Masters thesis]. Kansas State University; 2019. [cited 2021 Apr 14]. Available from: http://hdl.handle.net/2097/40267.

Council of Science Editors:

Xu L. Acceleration of the power and related methods with dynamic mode decomposition. [Masters Thesis]. Kansas State University; 2019. Available from: http://hdl.handle.net/2097/40267

15. Andrade Neto, Jayme. O problema do k-Autovalor em estudos de criticalidade.

Degree: 2018, Brazil

URL: http://hdl.handle.net/10183/196840

►

Neste trabalho o problema do cálculo do chamado fator de multiplicação em problemas de criticalidade de um reator nuclear, autovalor dominante k, em meio unidimensional… (more)

▼

Neste trabalho o problema do cálculo do chamado fator de multiplicação em problemas de criticalidade de um reator nuclear, autovalor dominante k, em meio unidimensional ) e tratado a partir de uma abordagem analítica. O método Analítico em Ordenadas Discretas, ADO, é aplicado através de duas metodologias distintas para a determinação do parâmetro k. Na primeira, a equação de transporte é resolvida incluindo o termo de fissão, em placa homogênea ou heterogênea, o que implica no aparecimento de constantes de separação complexas na região em que ocorre a fissão. Juntamente com condições de continuidade entre meios e condições de contorno, que podem ser do tipo vácuo ou reflexiva, a equação resultante para a determinação do parâmetro k é solucionada através do método iterativo da secante. Na segunda abordagem, a parcela correspondente a fissão na equação de transporte é considerada como um termo de fonte. A partir de estimativas iniciais para k e para essa fonte, um esquema similar ao Método da Potência é usado para se obter o valor do parâmetro k. Os resultados numéricos com a primeira abordagem são comparáveis aos resultados existentes na literatura, sendo obtidos com excelente precisão. Em geral, a partir de ordens de quadratura inferiores às disponíveis na literatura. As simulações com a segunda abordagem, apesar de evitarem soluções com parâmetros complexos, não obtiveram resultados com a mesma precisão da abordagem anterior.

In this work the problem of calculating the so called multiplication factor in criticality problems of a nuclear reactor, dominant eigenvalue k, in onedimensional slab is treated from an analytical approach. The Analytical Discrete Ordinates method, ADO, is applied through two different methodologies for the determination of the parameter k. Firstly, the transport equation is solved including the fission term, in homogeneous or heterogeneous slab. In such case there are complex separation constants in the region where fission occurs. In addition to boundary condition, continuity conditions on interface of regions are considered to write the resulting equation for determination of the parameter k that is solved by secant method, which is an iterative procedure. In the second approach, the fission term in the transport equation is considered as a source term. From initial estimates for k and for this source, a scheme similar to the Power Method is used to obtain the value of k. The numerical results with the first approach are comparable to the results in the literature and are obtained with excellent accuracy. In general, from lower orders of quadrature than those available in the literature. Simulations with the second approach, despite avoiding solutions with complex parameters, did not obtain results with the same precision than previous approach.

Advisors/Committee Members: Barichello, Liliane Basso.

Subjects/Keywords: Método analítico de ordenadas discretas; K-eigenvalue problem; Analytical discrete ordinates; Coarse-mesh finite difference

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APA (6^th Edition):

Andrade Neto, J. (2018). O problema do k-Autovalor em estudos de criticalidade. (Doctoral Dissertation). Brazil. Retrieved from http://hdl.handle.net/10183/196840

Chicago Manual of Style (16^th Edition):

Andrade Neto, Jayme. “O problema do k-Autovalor em estudos de criticalidade.” 2018. Doctoral Dissertation, Brazil. Accessed April 14, 2021. http://hdl.handle.net/10183/196840.

MLA Handbook (7^th Edition):

Andrade Neto, Jayme. “O problema do k-Autovalor em estudos de criticalidade.” 2018. Web. 14 Apr 2021.

Vancouver:

Andrade Neto J. O problema do k-Autovalor em estudos de criticalidade. [Internet] [Doctoral dissertation]. Brazil; 2018. [cited 2021 Apr 14]. Available from: http://hdl.handle.net/10183/196840.

Council of Science Editors:

Andrade Neto J. O problema do k-Autovalor em estudos de criticalidade. [Doctoral Dissertation]. Brazil; 2018. Available from: http://hdl.handle.net/10183/196840

Brigham Young University

16. Nelson, Curtis G. Diagonal Entry Restrictions in Minimum Rank Matrices, and the Inverse Inertia and Eigenvalue Problems for Graphs.

Degree: MS, 2012, Brigham Young University

URL: https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=4245&context=etd

► Let F be a field, let G be an undirected graph on n vertices, and let SF(G) be the set of all F-valued symmetric n… (more)

Subjects/Keywords: Combinatorial Matrix Theory; Diagonal Entry Restrictions; Graph; Inverse Eigenvalue Problem; Inverse Inertia Problem; Minimum Rank; Neutral; Nil; Nonzero; Symmetric; Mathematics

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APA (6^th Edition):

Nelson, C. G. (2012). Diagonal Entry Restrictions in Minimum Rank Matrices, and the Inverse Inertia and Eigenvalue Problems for Graphs. (Masters Thesis). Brigham Young University. Retrieved from https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=4245&context=etd

Chicago Manual of Style (16^th Edition):

Nelson, Curtis G. “Diagonal Entry Restrictions in Minimum Rank Matrices, and the Inverse Inertia and Eigenvalue Problems for Graphs.” 2012. Masters Thesis, Brigham Young University. Accessed April 14, 2021. https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=4245&context=etd.

MLA Handbook (7^th Edition):

Nelson, Curtis G. “Diagonal Entry Restrictions in Minimum Rank Matrices, and the Inverse Inertia and Eigenvalue Problems for Graphs.” 2012. Web. 14 Apr 2021.

Vancouver:

Nelson CG. Diagonal Entry Restrictions in Minimum Rank Matrices, and the Inverse Inertia and Eigenvalue Problems for Graphs. [Internet] [Masters thesis]. Brigham Young University; 2012. [cited 2021 Apr 14]. Available from: https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=4245&context=etd.

Council of Science Editors:

Nelson CG. Diagonal Entry Restrictions in Minimum Rank Matrices, and the Inverse Inertia and Eigenvalue Problems for Graphs. [Masters Thesis]. Brigham Young University; 2012. Available from: https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=4245&context=etd

University of Southern California

17. Meidani, Hadi. Uncertainty management for complex systems of systems: applications to the future smart grid.

Degree: PhD, Civil Engineering, 2014, University of Southern California

URL: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/94167/rec/7666

► Today, many of the infrastructures are composed of several coupled sub-systems, many of which are by themselves complex, and further couplings introduce yet more complexities… (more)

▼ Today, many of the infrastructures are composed of several coupled sub-systems, many of which are by themselves complex, and further couplings introduce yet more complexities which pose system operators with several challenging issues. In many of these infrastructure systems, uncertainty is an intrinsic features, whereas in several others it is merely a mathematical abstraction referring to our ignorance due either to the unknown governing physics or to missing information. A major challenge is the predictability of such complex systems of systems under these uncertainties and also the quantification of confidence in the prediction. A predictive science for these systems should (a) assess the uncertainties; that is, to identify and characterize them in the input variables or model parameters; and (b) predict their impacts on the performance of the system, which will eventually assist decision and policy making processes. This study aims to contribute to these two pillars of a successful predictive model for complex infrastructure systems. We have focused on the uncertainty management of the future Smart Grid, as an excellent example of a complex system of systems. The future Smart Grid will be a composition of interacting systems, including the power grid, the weather system, the social networks, the communication network, etc. Over the course of this study, the conceptual, mathematical and algorithmic challenges relevant to the establishment of a predictive science for this system have been examined and novel methodologies were developed to address these challenges. The scope of this dissertation includes the challenges induced by the uncertainties in the demand and supply sides of the future Smart Grid. Models for the characterization of these uncertainties have been proposed and their impacts on performance metrics of the overall system have been quantified. Advisors/Committee Members: Ghanem, Roger G. (Committee Chair), Masri, Sami F. (Committee Member), Rechenmacher, Amy Lynn (Committee Member), Becerik-Gerber, Burcin (Committee Member), Caire, Giuseppe (Committee Member).

Subjects/Keywords: uncertainty quantification; Markov chains; random eigenvalue problem; maximum entropy; consensus problem; systems of systems; robust decision making; smart grid; structural dynamics

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APA (6^th Edition):

Meidani, H. (2014). Uncertainty management for complex systems of systems: applications to the future smart grid. (Doctoral Dissertation). University of Southern California. Retrieved from http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/94167/rec/7666

Chicago Manual of Style (16^th Edition):

Meidani, Hadi. “Uncertainty management for complex systems of systems: applications to the future smart grid.” 2014. Doctoral Dissertation, University of Southern California. Accessed April 14, 2021. http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/94167/rec/7666.

MLA Handbook (7^th Edition):

Meidani, Hadi. “Uncertainty management for complex systems of systems: applications to the future smart grid.” 2014. Web. 14 Apr 2021.

Vancouver:

Meidani H. Uncertainty management for complex systems of systems: applications to the future smart grid. [Internet] [Doctoral dissertation]. University of Southern California; 2014. [cited 2021 Apr 14]. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/94167/rec/7666.

Council of Science Editors:

Meidani H. Uncertainty management for complex systems of systems: applications to the future smart grid. [Doctoral Dissertation]. University of Southern California; 2014. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/94167/rec/7666

KTH

18. Ugarte, Crystal. A numerical investigation of Anderson localization in weakly interacting Bose gases.

Degree: NA, 2020, KTH

URL: http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-269167

►

The ground state of a quantum system is the minimizer of the total energy of that system. The aim of this thesis is to… (more)

▼

The ground state of a quantum system is the minimizer of the total energy of that system. The aim of this thesis is to present and numerically solve the Gross-Pitaevskii eigenvalue problem (GPE) as a physical model for the formation of ground states of dilute Bose gases at ultra-low temperatures in a disordered potential. The first part of the report introduces the quantum mechanical phenomenon that arises at ground states of the Bose gases; the Anderson localization, and presents the nonlinear eigenvalue problem and the finite element method (FEM) used to discretize the GPE. The numerical method used to solve the eigenvalue problem for the smallest eigenvalue is called the inverse power iteration method, which is presented and explained. In the second part of the report, the smallest eigenvalue of a linear Schrödinger equation is compared with the numerically computed smallest eigenvalue (ground state) in order to evaluate the accuracy of a linear numerical scheme constructed as first step for numerically solving the non-linear problem. In the next part of the report, the numerical methods are implemented to solve for the eigenvalue and eigenfunction of the (non-linear) GPE at ground state (smallest eigenvalue). The mathematical expression for the quantum energy and smallest eigenvalue of the non-linear system are presented in the report. The methods used to solve the GPE are the FEM and inverse power iteration method and different instances of the Anderson localization are produced. The study shows that the error of the smallest eigenvalue approximation for the linear case without disorder is satisfying when using FEM and Power iteration method. The accuracy of the approximation obtained for the linear case without disorder is satisfying, even for a low numbers of iterations. The methods require many more iterations for solving the GPE with a strong disorder. On the other hand, pronounced instances of Anderson localizations are produced in a certain scaling regime. The study shows that the GPE indeed works well as a physical model for the Anderson localization.

Syftet med denna avhandling är att undersöka hur väl Gross-Pitaevskii egenvärdesekvation (GPE) passar som en fysisk modell för bildandet av stationära elektronstater i utspädda Bose-gaser vid extremt låga temperaturer. Fenomenet som skall undersökas heter Anderson lokalisering och uppstår när potentialfältets styrka och störning i systemet är tillräckligt hög. Undersökningen görs i denna avhandling genom att numeriskt lösa GPE samt illustrera olika utfall av Anderson lokaliseringen vid olika numeriska värden. Den första delen av rapporten introducerar det icke-linjära matematiska uttrycket för GPE samt de numeriska metoderna som används för att lösa problemet numerisk: finita elementmetoden (FEM) samt egenvärdesalgoritmen som heter inversiiteration. Finita elementmetoden används för att diskretisera variationsproblemet av GPE och ta fram en enkel algebraisk ekvation. Egenvärdesalgoritmen tillämpas på den algebraiska ekvation för att iterativt…

Subjects/Keywords: Applied mathematics; finite elements; eigenvalue solver; eigenvalue problem; Bose-Einstein Codensate; Finita elementmetoden; tillämpad matematik; Bose-Einstein kondensat; egenvärdesalgoritm; egenvärdesproblem; Mathematics; Matematik

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APA (6^th Edition):

Ugarte, C. (2020). A numerical investigation of Anderson localization in weakly interacting Bose gases. (Thesis). KTH. Retrieved from http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-269167

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Ugarte, Crystal. “A numerical investigation of Anderson localization in weakly interacting Bose gases.” 2020. Thesis, KTH. Accessed April 14, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-269167.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Ugarte, Crystal. “A numerical investigation of Anderson localization in weakly interacting Bose gases.” 2020. Web. 14 Apr 2021.

Vancouver:

Ugarte C. A numerical investigation of Anderson localization in weakly interacting Bose gases. [Internet] [Thesis]. KTH; 2020. [cited 2021 Apr 14]. Available from: http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-269167.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Ugarte C. A numerical investigation of Anderson localization in weakly interacting Bose gases. [Thesis]. KTH; 2020. Available from: http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-269167

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

19. Genseberger, M. Domain decomposition in the Jacobi-Davidson method for eigenproblems.

Degree: 2001, University Utrecht

URL: https://dspace.library.uu.nl/handle/1874/861 ; URN:NBN:NL:UI:10-1874-861 ; 1874/861 ; URN:NBN:NL:UI:10-1874-861 ; https://dspace.library.uu.nl/handle/1874/861

► Grootschalige eigenwaardeproblemen spelen een belangrijke rol in wetenschappelijk onderzoek naar een breed scala van fenomenen. Deze fenomenen hebben vaak niet de belangstelling van wetenschappers alleen,… (more)

▼ Grootschalige eigenwaardeproblemen spelen een belangrijke rol in wetenschappelijk onderzoek naar een breed scala van fenomenen. Deze fenomenen hebben vaak niet de belangstelling van wetenschappers alleen, het betreffen ook verschijnselen die regelmatig in het nieuws komen zoals klimaatverandering en aardbevingen. Voor het berekenen van oplossingen voor grootschalige eigenwaardeproblemen is de afgelopen twee decennia een aanzienlijke vooruitgang gemaakt met de ontwikkeling van numerieke methoden. Een van de meest attractieve methoden is de Jacobi-Davidson methode. De Jacobi-Davidson methode reduceert een groot eigenwaardeprobleem tot een klein probleem door het te projecteren op een geschikte laag dimensionale deelruimte. Benaderende oplossingen voor het grote probleem worden verkregen door middel van hoge precisie oplossingen van het kleine probleem. De crux van de methode is hoe de deelruimte wordt uitgebreid. De uitbreidingsvector van de deelruimte wordt berekend uit de zogenaamde correctie vergelijking. Het leven is helaas niet zo gemakkelijk: de correctie vergelijking op zichzelf vormt een groot lineair stelsel, met afmetingen gelijk aan die van het oorspronkelijke grote eigenwaardeprobleem. Dit is de reden dat het meeste rekenwerk van de Jacobi-Davidson methode voortkomt uit het berekenen van (benaderende) oplossingen voor de correctie vergelijking. Het proefschrift houdt zich bezig met de vraag hoe een preconditioneerder gebaseerd op domeindecompositie in de Jacobi-Davidson methode kan worden ingebed om het leven wat te veraangenamen voor PDV-achtige eigenwaardeproblemen. Eerst worden in hoofdstuk 2 alternatieve correctie vergelijkingen voor de Jacobi-Davidson methode zonder reconditionering bestudeerd. Motivatie voor deze studie is de analogie met de geneste iteratieve methoden GMRESR en GCRO voor lineaire systemen. Bovendien kan het een remedie zijn in geval van een meervoudige eigenwaarde. Na deze pilotstudie is het kader geschetst voor het inbedden van de domeindecompositie techniek in de Jacobi-Davidson methode. De techniek is gebaseerd op eerder werk van W.P. Tang en K.H. Tan & M.J.A. Borsboom voor lineaire systemen. Voor een lineair systeem heeft W.P. Tang voorgesteld het systeem met copieen van de onbekenden bij de interne rand tussen de subdomeinen uit te breiden om zo een additieve Schwarz methode met minimale overlap mogelijk te maken. K.H. Tan & M.J.A. Borsboom hebben dit idee verder verfijnd door in plaats van copieen juist virtuele onbekenden te introduceren voor deze onbekenden. Op deze manier worden extra vrijheidsgraden gecreeerd, die zich terugvertalen in koppelingsvergelijkingen voor onbekenden en virtuele tegenhangers bij de interne rand. Het idee is nu om deze koppelingsvergelijkingen af te stemmen voor het onderliggende eigenwaardeprobleem om zo de convergentie van de oplossingsmethode te versnellen. Echter, in de correctie vergelijking komt een operator voor waarbij een matrix is opgeschoven met een benaderende eigenwaarde. Daarom is speciale aandacht vereist bij het…

Subjects/Keywords: Eigenvalue problem; domain decomposition; iterative method; Jacobi-Davidson; Schwarz method; eigenvalue; eigenvector

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Genseberger, M. (2001). Domain decomposition in the Jacobi-Davidson method for eigenproblems. (Doctoral Dissertation). University Utrecht. Retrieved from https://dspace.library.uu.nl/handle/1874/861 ; URN:NBN:NL:UI:10-1874-861 ; 1874/861 ; URN:NBN:NL:UI:10-1874-861 ; https://dspace.library.uu.nl/handle/1874/861

Chicago Manual of Style (16^th Edition):

Genseberger, M. “Domain decomposition in the Jacobi-Davidson method for eigenproblems.” 2001. Doctoral Dissertation, University Utrecht. Accessed April 14, 2021. https://dspace.library.uu.nl/handle/1874/861 ; URN:NBN:NL:UI:10-1874-861 ; 1874/861 ; URN:NBN:NL:UI:10-1874-861 ; https://dspace.library.uu.nl/handle/1874/861.

MLA Handbook (7^th Edition):

Genseberger, M. “Domain decomposition in the Jacobi-Davidson method for eigenproblems.” 2001. Web. 14 Apr 2021.

Vancouver:

Genseberger M. Domain decomposition in the Jacobi-Davidson method for eigenproblems. [Internet] [Doctoral dissertation]. University Utrecht; 2001. [cited 2021 Apr 14]. Available from: https://dspace.library.uu.nl/handle/1874/861 ; URN:NBN:NL:UI:10-1874-861 ; 1874/861 ; URN:NBN:NL:UI:10-1874-861 ; https://dspace.library.uu.nl/handle/1874/861.

Council of Science Editors:

Genseberger M. Domain decomposition in the Jacobi-Davidson method for eigenproblems. [Doctoral Dissertation]. University Utrecht; 2001. Available from: https://dspace.library.uu.nl/handle/1874/861 ; URN:NBN:NL:UI:10-1874-861 ; 1874/861 ; URN:NBN:NL:UI:10-1874-861 ; https://dspace.library.uu.nl/handle/1874/861

20. Hochstenbach, Michiel Erik. Subspace Methods for Eigenvalue Problems.

Degree: 2003, University Utrecht

URL: https://dspace.library.uu.nl/handle/1874/881 ; URN:NBN:NL:UI:10-1874-881 ; 1874/881 ; URN:NBN:NL:UI:10-1874-881 ; https://dspace.library.uu.nl/handle/1874/881

► This thesis treats a number of aspects of subspace methods for various eigenvalue problems. Vibrations and their corresponding eigenvalues (or frequencies) arise in science, engineering,… (more)

Subjects/Keywords: eigenvalue problem; subspace method; Jacobi-Davidson; Lanczos; two-sided subspace method; large sparse matrix; generalized eigenproblem; singular value decomposition; polynomial eigenvalue problem; multiparameter eigenvalue problem

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Hochstenbach, M. E. (2003). Subspace Methods for Eigenvalue Problems. (Doctoral Dissertation). University Utrecht. Retrieved from https://dspace.library.uu.nl/handle/1874/881 ; URN:NBN:NL:UI:10-1874-881 ; 1874/881 ; URN:NBN:NL:UI:10-1874-881 ; https://dspace.library.uu.nl/handle/1874/881

Chicago Manual of Style (16^th Edition):

Hochstenbach, Michiel Erik. “Subspace Methods for Eigenvalue Problems.” 2003. Doctoral Dissertation, University Utrecht. Accessed April 14, 2021. https://dspace.library.uu.nl/handle/1874/881 ; URN:NBN:NL:UI:10-1874-881 ; 1874/881 ; URN:NBN:NL:UI:10-1874-881 ; https://dspace.library.uu.nl/handle/1874/881.

MLA Handbook (7^th Edition):

Hochstenbach, Michiel Erik. “Subspace Methods for Eigenvalue Problems.” 2003. Web. 14 Apr 2021.

Vancouver:

Hochstenbach ME. Subspace Methods for Eigenvalue Problems. [Internet] [Doctoral dissertation]. University Utrecht; 2003. [cited 2021 Apr 14]. Available from: https://dspace.library.uu.nl/handle/1874/881 ; URN:NBN:NL:UI:10-1874-881 ; 1874/881 ; URN:NBN:NL:UI:10-1874-881 ; https://dspace.library.uu.nl/handle/1874/881.

Council of Science Editors:

Hochstenbach ME. Subspace Methods for Eigenvalue Problems. [Doctoral Dissertation]. University Utrecht; 2003. Available from: https://dspace.library.uu.nl/handle/1874/881 ; URN:NBN:NL:UI:10-1874-881 ; 1874/881 ; URN:NBN:NL:UI:10-1874-881 ; https://dspace.library.uu.nl/handle/1874/881

NSYSU

21. Zhu, Jun-hui. Design and Characterization of Laser Resonators with Intra-cavity Azimuthal Symmetry-breaking optics.

Degree: Master, Electro-Optical Engineering, 2016, NSYSU

URL: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0612116-132113

► Optical vortex (OV) is more than a beam of donor-shaped intensity pro- file. It carries well-defined orbital angular momentum (OAM) in the photons within. The… (more)

▼ Optical vortex (OV) is more than a beam of donor-shaped intensity pro- file. It carries well-defined orbital angular momentum (OAM) in the photons within. The unique property of OV beam have attracted growing attentions due to the wide range of promising applications including microscopy, particle manipulation, astronomy, cosmology and sub-Peta hertz bit-rate optical communications. Although a number of techniques are devised to generate OV with helical wavefront from gaussian beams by exploiting external resonator conversion element such as spiral phase plate (SPP), holograms, anisotropic media (Q-plate), not one of these approaches achieve a satisfactory conversion efficiency and beam quality. Ray transfer matrix (RTM) are widely adopted technique to analyses the property of a laser resonator of paraxial bundles of lights. Nonetheless, the inhomogeneous feature of azimuthal symmetry breaking (ASB) element make the resonator design a difficult problem. In this study we develop an iterative approach to solve the nonlinear eigenvalue problem in laser resonator with intra-cavity ASB elements within. This approach efficiently identify the trajectories of stable periodic orbitals (modes) of ASB laser resonators of arbitrary order N. Manipulation of the trajectories is accomplished by tuning the cavity parameters such as radius of curvature of the cavity mirror, cavity length and the position of the ASB element inside the cavity. Notably the specific relative angular momentum (SRAM, angular mom- entum over mass) in the orbital is obtained with a proposed specious particle model for the trajectories. The SRAM introduced by the SPP is investigated to be linearly to the pitch height of the SPP. It is in good agreement in wave-optics picture, in which the pitch directly indicates the topological charge carried by the SPP. Further phase space characterization of the cavity orbitals is considered for possible chaotic orbitals and scar modes to mimic the quantum billiard problem in ASB laser resonator in classical way. Advisors/Committee Members: Shou-Tai Lin (chair), Yuan-Yao Lin (committee member), Yen-Yin Lin (chair).

Subjects/Keywords: spiral phase plate; azimuthal symmetry breaking; nonlinear eigenvalue problem; specific relative angular momentum; ray transfer matrix; optical vortex; orbital angular momentum

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APA (6^th Edition):

Zhu, J. (2016). Design and Characterization of Laser Resonators with Intra-cavity Azimuthal Symmetry-breaking optics. (Thesis). NSYSU. Retrieved from http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0612116-132113

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Zhu, Jun-hui. “Design and Characterization of Laser Resonators with Intra-cavity Azimuthal Symmetry-breaking optics.” 2016. Thesis, NSYSU. Accessed April 14, 2021. http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0612116-132113.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Zhu, Jun-hui. “Design and Characterization of Laser Resonators with Intra-cavity Azimuthal Symmetry-breaking optics.” 2016. Web. 14 Apr 2021.

Vancouver:

Zhu J. Design and Characterization of Laser Resonators with Intra-cavity Azimuthal Symmetry-breaking optics. [Internet] [Thesis]. NSYSU; 2016. [cited 2021 Apr 14]. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0612116-132113.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Zhu J. Design and Characterization of Laser Resonators with Intra-cavity Azimuthal Symmetry-breaking optics. [Thesis]. NSYSU; 2016. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0612116-132113

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Indian Institute of Science

22. Choudhary, Shalu. Numerical Methods For Solving The Eigenvalue Problem Involved In The Karhunen-Loeve Decomposition.

Degree: MSc Engg, Faculty of Engineering, 2014, Indian Institute of Science

URL: http://etd.iisc.ac.in/handle/2005/2308

► In structural analysis and design it is important to consider the effects of uncertainties in loading and material properties in a rational way. Uncertainty in… (more)

▼ In structural analysis and design it is important to consider the effects of uncertainties in loading and material properties in a rational way. Uncertainty in material properties such as heterogeneity in elastic and mass properties can be modeled as a random field. For computational purpose, it is essential to discretize and represent the random field. For a field with known second order statistics, such a representation can be achieved by Karhunen-Lo`eve (KL) expansion. Accordingly, the random field is represented in a truncated series expansion using a few eigenvalues and associated eigenfunctions of the covariance function, and corresponding random coefficients. The eigenvalues and eigenfunctions of the covariance kernel are obtained by solving a second order Fredholm integral equation. A closed-form solution for the integral equation, especially for arbitrary domains, may not always be available. Therefore an approximate solution is sought. While finding an approximate solution, it is important to consider both accuracy of the solution and the cost of computing the solution. This work is focused on exploring a few numerical methods for estimating the solution of this integral equation. Three different methods:(i)using finite element bases(Method1),(ii) mid-point approximation(Method2), and(iii)by the Nystr¨om method(Method3), are implemented and numerically studied. The methods and results are compared in terms of accuracy, computational cost, and difficulty of implementation. In the first method an eigenfunction is first represented in a linear combination of a set of finite element bases. The resulting error in the integral equation is then minimized in the Galerkinsense, which results in a generalized matrix eigenvalue problem. In the second method, the domain is partitioned into a finite number of subdomains. The covariance function is discretized by approximating its value over each subdomain locally, and thereby the integral equation is transformed to a matrix eigenvalue problem. In the third method the Fredholm integral equation is approximated by a quadrature rule, which also results in a matrix eigenvalue problem. The methods and results are compared in terms of accuracy, computational cost, and difficulty of implementation. The first part of the numerical study involves comparing these three methods. This numerical study is first done in one dimensional domain. Then for study in two dimensions a simple rectangular domain(referred toasDomain1)is taken with an uncertain material property modeled as a Gaussian random field. For the chosen covariance model and domain, the analytical solutions are known, which allows verifying the accuracy of the numerical solutions. There by these three numerical methods are studied and are compared for a chosen target accuracy and different correlation lengths of the random field. It was observed that Method 2 and Method 3 are much faster than the Method 1. On the other hand, for Method 2 and 3, additional cost for discretizing the domain into nodes should be considered… Advisors/Committee Members: Ghosh, Debraj (advisor).

Subjects/Keywords: Karhunen-Loeve Decomposition; Eigenvalue Problem; Numerical Analysis; Structural Analysis (Engineering); Eigenfunctions; Eigenvalues; Gaussian Random Field; Structural Engineering

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Choudhary, S. (2014). Numerical Methods For Solving The Eigenvalue Problem Involved In The Karhunen-Loeve Decomposition. (Masters Thesis). Indian Institute of Science. Retrieved from http://etd.iisc.ac.in/handle/2005/2308

Chicago Manual of Style (16^th Edition):

Choudhary, Shalu. “Numerical Methods For Solving The Eigenvalue Problem Involved In The Karhunen-Loeve Decomposition.” 2014. Masters Thesis, Indian Institute of Science. Accessed April 14, 2021. http://etd.iisc.ac.in/handle/2005/2308.

MLA Handbook (7^th Edition):

Choudhary, Shalu. “Numerical Methods For Solving The Eigenvalue Problem Involved In The Karhunen-Loeve Decomposition.” 2014. Web. 14 Apr 2021.

Vancouver:

Choudhary S. Numerical Methods For Solving The Eigenvalue Problem Involved In The Karhunen-Loeve Decomposition. [Internet] [Masters thesis]. Indian Institute of Science; 2014. [cited 2021 Apr 14]. Available from: http://etd.iisc.ac.in/handle/2005/2308.

Council of Science Editors:

Choudhary S. Numerical Methods For Solving The Eigenvalue Problem Involved In The Karhunen-Loeve Decomposition. [Masters Thesis]. Indian Institute of Science; 2014. Available from: http://etd.iisc.ac.in/handle/2005/2308

Washington State University

23. [No author]. On the computation of eigenvalues, spectral bounds, and Hessenberg form for matrix polynomials .

Degree: 2016, Washington State University

URL: http://hdl.handle.net/2376/12050

► In this dissertation we focus on root-finding methods, such as Laguerre's method, for solving the polynomial eigenvalue problem. Serious consideration is given to the initial… (more)

Subjects/Keywords: Mathematics; Hessenberg form; Laguerre's method; matrix polynomials; polynomial eigenvalue problem; root finding algorithm; Unitary matrix polynomials

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APA (6^th Edition):

author], [. (2016). On the computation of eigenvalues, spectral bounds, and Hessenberg form for matrix polynomials . (Thesis). Washington State University. Retrieved from http://hdl.handle.net/2376/12050

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

author], [No. “On the computation of eigenvalues, spectral bounds, and Hessenberg form for matrix polynomials .” 2016. Thesis, Washington State University. Accessed April 14, 2021. http://hdl.handle.net/2376/12050.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

author], [No. “On the computation of eigenvalues, spectral bounds, and Hessenberg form for matrix polynomials .” 2016. Web. 14 Apr 2021.

Vancouver:

author] [. On the computation of eigenvalues, spectral bounds, and Hessenberg form for matrix polynomials . [Internet] [Thesis]. Washington State University; 2016. [cited 2021 Apr 14]. Available from: http://hdl.handle.net/2376/12050.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

author] [. On the computation of eigenvalues, spectral bounds, and Hessenberg form for matrix polynomials . [Thesis]. Washington State University; 2016. Available from: http://hdl.handle.net/2376/12050

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Université Montpellier II

24. Wieczorek, Kerstin. Numerical Study of Mach Number Effects on Combustion Instability : Etude numérique des effets du nombre de Mach sur les instabilités de combustion.

Degree: Docteur es, Mathématiques appliquées et applications des mathématiques, 2010, Université Montpellier II

URL: http://www.theses.fr/2010MON20106

►

L'évolution des turbines à gaz vers des régimes de combustion en mélange pauvre augmente la sensibilité de la flamme aux perturbations de l'écoulement. Plus particulièrement,… (more)

▼

L'évolution des turbines à gaz vers des régimes de combustion en mélange pauvre augmente la sensibilité de la flamme aux perturbations de l'écoulement. Plus particulièrement, cela augmente le risque que des instabilités de combustion apparaissent. Comme ces oscillations peuvent affecter le processus de combustion, il est très important d'être capable de prédire ce comportement au niveau de la conception.L'objectif du travail présenté est de développer un solveur numérique qui permet de décrire ces instabilités, et d'évaluer les effets du nombre de Mach de l'écoulement moyen sur ce phénomène. L'approche choisie consiste à résoudre les équations d'Euler linéarisées, qui sont écrites dans le domaine fréquentiel sous la forme d'un problème aux valeurs propres. Ce système d'équations permets de prendre en compte la vitesse moyenne de l'écoulement, et donc d'évaluer les effets causés par la convection et leur impact sur la stabilité des modes. Parmi les mécanismes qui peuvent être étudiés se trouve notamment l'effet des ondes d'entropie convectées, ce qui est particulièrement intéressant dans le contexte des chambres de combustions. Afin de déterminer l'effet des termes liés à la vitesse de l'écoulement moyen sur la stabilité des modes, une analyse de l'énergie contenue dans les perturbations est effectuée. Finalement, l'aspect de la non-orthogonalité des modes propres, qui permet une croissance d'énergie transitoire dans un système linéairement stable, est abordé.

The development of gas turbines towards lean combustion increases the susceptibility of the flame to flow perturbations, and leads more particularly to a higher risk of combustion instability. As these self-sustained oscillations may affect the performance of the combustion device, it is very important to be able to predict them at the design level. At present, several methods are used to describe combustion instabilities, ranging from complex LES and DNS calculations to low-order network models. An intermediate method consists in solving a set of equations describing the acoustic field using a finite volume technique, which is the approach used in the present study.This thesis discusses the impact of a non zero Mach number mean flow field on thermoacoustic instability. The study is based on the linearized Euler equations, which are stated in the frequency domain in the form of an eigenvalue problem. Using the linearized Euler equations rather than the Helmholtz equation avoids making the commonly used assumption of the mean flow being at rest, and allows to take into account convection effects and their impact on the stability of the system. Among the mechanisms that can be studied using the present approach is namely the impact of convected entropy waves, which is especially interesting in combustion applications.For this study, a 1D and a 2D numerical solver have been developed and are presented in this thesis. In order to asses the effect of the mean flow terms on the modes' stability, an analysis of the disturbance energy budget is performed. Finally,…

Advisors/Committee Members: Nicoud, Franck (thesis director).

Subjects/Keywords: Acoustique; Instabilité de Combustion; Equations d'Euler linéarisées; Problème aux valeurs propres; Acoustics; Combustion Instability; Linearized Euler Equations; Eigenvalue Problem

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APA (6^th Edition):

Wieczorek, K. (2010). Numerical Study of Mach Number Effects on Combustion Instability : Etude numérique des effets du nombre de Mach sur les instabilités de combustion. (Doctoral Dissertation). Université Montpellier II. Retrieved from http://www.theses.fr/2010MON20106

Chicago Manual of Style (16^th Edition):

Wieczorek, Kerstin. “Numerical Study of Mach Number Effects on Combustion Instability : Etude numérique des effets du nombre de Mach sur les instabilités de combustion.” 2010. Doctoral Dissertation, Université Montpellier II. Accessed April 14, 2021. http://www.theses.fr/2010MON20106.

MLA Handbook (7^th Edition):

Wieczorek, Kerstin. “Numerical Study of Mach Number Effects on Combustion Instability : Etude numérique des effets du nombre de Mach sur les instabilités de combustion.” 2010. Web. 14 Apr 2021.

Vancouver:

Wieczorek K. Numerical Study of Mach Number Effects on Combustion Instability : Etude numérique des effets du nombre de Mach sur les instabilités de combustion. [Internet] [Doctoral dissertation]. Université Montpellier II; 2010. [cited 2021 Apr 14]. Available from: http://www.theses.fr/2010MON20106.

Council of Science Editors:

Wieczorek K. Numerical Study of Mach Number Effects on Combustion Instability : Etude numérique des effets du nombre de Mach sur les instabilités de combustion. [Doctoral Dissertation]. Université Montpellier II; 2010. Available from: http://www.theses.fr/2010MON20106

25. Neely, Kara. Towards the Resolution of an Eigenvalue Problem for the 2-Hessian Operator.

Degree: 2014, University of Illinois – Chicago

URL: http://hdl.handle.net/10027/11263

► The motivation for the work done in this thesis is the resolution of an eigenvalue problem for the 2-Hessian operator. In order to be in… (more)

Subjects/Keywords: 2-Hessian; Monge-Ampere; eigenvalue problem

…dimensional Poisson equation. Another problem similar to (Equation 1.2) is the eigenvalue… …problem for the Poisson equation, also known as the Lapacian eigenvalue problem. This is solved… …0.0008731 1.974998883 CHAPTER 3 THE LAPLACIAN EIGENVALUE PROBLEM The Laplace operator or… …propagation, and quantum mechanics (Sauer, 2006). The Laplacian eigenvalue problem is ∆u… …domain Ω = [0, 1]m that will be reduced to a simple matrix eigenvalue problem. We…

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Neely, K. (2014). Towards the Resolution of an Eigenvalue Problem for the 2-Hessian Operator. (Thesis). University of Illinois – Chicago. Retrieved from http://hdl.handle.net/10027/11263

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Neely, Kara. “Towards the Resolution of an Eigenvalue Problem for the 2-Hessian Operator.” 2014. Thesis, University of Illinois – Chicago. Accessed April 14, 2021. http://hdl.handle.net/10027/11263.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Neely, Kara. “Towards the Resolution of an Eigenvalue Problem for the 2-Hessian Operator.” 2014. Web. 14 Apr 2021.

Vancouver:

Neely K. Towards the Resolution of an Eigenvalue Problem for the 2-Hessian Operator. [Internet] [Thesis]. University of Illinois – Chicago; 2014. [cited 2021 Apr 14]. Available from: http://hdl.handle.net/10027/11263.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Neely K. Towards the Resolution of an Eigenvalue Problem for the 2-Hessian Operator. [Thesis]. University of Illinois – Chicago; 2014. Available from: http://hdl.handle.net/10027/11263

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

26. Ellard, Richard. Spectral properties of nonnegative matrices.

Degree: 2017, University College Dublin. School of Mathematics and Statistics

URL: http://hdl.handle.net/10197/8597

► The spectral properties of nonnegative matrices have intrigued pure and applied mathematicians alike, beginning with the classical works of Oskar Perron and Georg Frobenius at… (more)

▼ The spectral properties of nonnegative matrices have intrigued pure and applied mathematicians alike, beginning with the classical works of Oskar Perron and Georg Frobenius at the start of the twentieth century. One question which stems naturally from this area of research is that of the "Nonnegative Inverse Eigenvalue Problem", or NIEP. This is the problem of characterising those lists of complex numbers which are "realisable" as the spectrum of some entrywise nonnegative matrix. This thesis explores the NIEP, as well as one of its variants, the "Symmetric Nonnegative Inverse Eigenvalue Problem", or SNIEP, which considers realisability by a symmetric nonnegative matrix.The question of determining which operations on lists preserve realisability is pertinent in the NIEP, since such operations can allow us to construct more complicated lists from simple building blocks. We present some new results along these lines. In particular, we discuss how to replace parts of realisable lists by longer lists, while preserving realisability.In those cases where a realising matrix is known to exist, one can consider studying the properties of this matrix. We focus our attention on the problem of characterising the diagonal elements of the realising matrix and achieve a complete solution in the case where every entry in the list (apart from the Perron eigenvalue) has nonpositive real part. In order to prove this result, we derived complex analogues of Newton's inequalities, which are of independent interest.In the context of the SNIEP, we unify a large body of research by presenting a recursive method for constructing symmetrically realisable lists and showing that essentially all previously know sufficient conditions are either contained in, or equivalent to the family we introduce. Our construction also reveals several interesting properties of the family in question and allows for an explicit algorithmic characterisation of the lists that lie within it.Finally, we construct families of symmetrically realisable lists which do not satisfy any previously known sufficient conditions. Advisors/Committee Members: Smigoc, Helena.

Subjects/Keywords: Diagonal Elements; Matrix Theory; Newton's Inequalities; Nonnegative Inverse Eigenvalue Problem; Nonnegative Matrices; Soules Matrix; 0|aNon-negative matrices.; #0|aEigenvalues.

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APA (6^th Edition):

Ellard, R. (2017). Spectral properties of nonnegative matrices. (Thesis). University College Dublin. School of Mathematics and Statistics . Retrieved from http://hdl.handle.net/10197/8597

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Ellard, Richard. “Spectral properties of nonnegative matrices.” 2017. Thesis, University College Dublin. School of Mathematics and Statistics . Accessed April 14, 2021. http://hdl.handle.net/10197/8597.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Ellard, Richard. “Spectral properties of nonnegative matrices.” 2017. Web. 14 Apr 2021.

Vancouver:

Ellard R. Spectral properties of nonnegative matrices. [Internet] [Thesis]. University College Dublin. School of Mathematics and Statistics ; 2017. [cited 2021 Apr 14]. Available from: http://hdl.handle.net/10197/8597.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Ellard R. Spectral properties of nonnegative matrices. [Thesis]. University College Dublin. School of Mathematics and Statistics ; 2017. Available from: http://hdl.handle.net/10197/8597

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

27. Poulson, Jack Lesly. Formalized parallel dense linear algebra and its application to the generalized eigenvalue problem.

Degree: MSin Engineering, Aerospace Engineering, 2009, University of Texas – Austin

URL: http://hdl.handle.net/2152/ETD-UT-2009-05-139

► This thesis demonstrates an efficient parallel method of solving the generalized eigenvalue problem, KΦ = M ΦΛ, where K is symmetric and M is symmetric… (more)

Subjects/Keywords: generalized eigenvalue problem; parallel dense linear algebra

…generalized eigenvalue problem (EVP) is the search for nontrivial solutions to Ax = λBx… …standard form eigenvalue problem in parallel, Hendrickson, Jessup, and Smith[16]… …of the new algorithm for the reduction of the generalized eigenvalue problem to standard… …eigenpair (λ, x) ∈ R × Rn . λ is called an eigenvalue of the system, and x is referred… …to as an eigenvector[20]. If one wishes to find multiple eigenpairs, the problem…

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APA (6^th Edition):

Poulson, J. L. (2009). Formalized parallel dense linear algebra and its application to the generalized eigenvalue problem. (Masters Thesis). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/ETD-UT-2009-05-139

Chicago Manual of Style (16^th Edition):

Poulson, Jack Lesly. “Formalized parallel dense linear algebra and its application to the generalized eigenvalue problem.” 2009. Masters Thesis, University of Texas – Austin. Accessed April 14, 2021. http://hdl.handle.net/2152/ETD-UT-2009-05-139.

MLA Handbook (7^th Edition):

Poulson, Jack Lesly. “Formalized parallel dense linear algebra and its application to the generalized eigenvalue problem.” 2009. Web. 14 Apr 2021.

Vancouver:

Poulson JL. Formalized parallel dense linear algebra and its application to the generalized eigenvalue problem. [Internet] [Masters thesis]. University of Texas – Austin; 2009. [cited 2021 Apr 14]. Available from: http://hdl.handle.net/2152/ETD-UT-2009-05-139.

Council of Science Editors:

Poulson JL. Formalized parallel dense linear algebra and its application to the generalized eigenvalue problem. [Masters Thesis]. University of Texas – Austin; 2009. Available from: http://hdl.handle.net/2152/ETD-UT-2009-05-139

Princeton University

28. Avanesyan, Levon. Optimal investment in incomplete markets with multiple Brownian externalities .

Degree: PhD, 2021, Princeton University

URL: http://arks.princeton.edu/ark:/88435/dsp01m613n165k

► An investor’s optimal market portfolio is shaped by their investment performance criterion. The latter is largely determined by the investor's idiosyncratic objectives and preferences. This… (more)

▼ An investor’s optimal market portfolio is shaped by their investment performance criterion. The latter is largely determined by the investor's idiosyncratic objectives and preferences. This dissertation contributes to the study of optimal investment under the expected utility of terminal wealth (Merton), as well as forward performance criteria. Our set-up is that of a continuous incomplete stock market model, where the incompleteness stems from multiple Brownian externalities. The externalities manifest themselves through the stock return and volatility coefficients, either explicitly by driving observable stochastic factors or implicitly by increasing the market filtration. In a Markovian multifactor market model we introduce the eigenvalue equality (EVE) stock-factor correlation structure, and construct a large class of forward performance processes (FPPs) with power-utility initial data, as well as their corresponding optimal portfolios. This is done by solving the associated non-linear parabolic partial differential equations (PDEs) posed in the ``wrong'' time direction. We establish on domains an explicit form of the generalized Widder's theorem of Nadtochiy and Tehranchi (Math. Financ. 27:438-470, 2015, Theorem 3.12) and rely hereby on the Laplace inversion in time of the solutions to suitable linear parabolic PDEs posed in the ``right'' time direction. Next, we consider the Merton problem with power utility in a market model with the stock coefficients adapted to a factor-generated filtration. This setup admits market models with non-semimartingale factors. For models with EVE structure we find the optimal portfolio weights up to the computation of a certain conditional expectation, and explain how to evaluate the latter in affine Volterra factor models. We extend these results to a general stock-factor correlation setting for, what we will call, Sharpe ratio separable (SRS) market models. In our most general market model, we construct a broad class of FPPs with initial conditions of power mixture type, u(x) = ∈t_\mathbb{I} \frac{x^1-γ}{1-γ }ν(\dd γ). We derive the properties of two-power mixture FPPs when the risk aversion coefficients are continuous stochastic processes in (0,1), and provide a full characterization when the coefficients are constants. Finally, we discuss the problem of managing an investment pool of two investors, whose respective preferences evolve as power FPPs. Advisors/Committee Members: Shkolnikov, Mykhaylo (advisor), Sircar, Ronnie (advisor).

Subjects/Keywords: eigenvalue equality correlation structure; forward performance process; merton problem; multiple externalities; power mixture; sharpe ratio separable model

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Avanesyan, L. (2021). Optimal investment in incomplete markets with multiple Brownian externalities . (Doctoral Dissertation). Princeton University. Retrieved from http://arks.princeton.edu/ark:/88435/dsp01m613n165k

Chicago Manual of Style (16^th Edition):

Avanesyan, Levon. “Optimal investment in incomplete markets with multiple Brownian externalities .” 2021. Doctoral Dissertation, Princeton University. Accessed April 14, 2021. http://arks.princeton.edu/ark:/88435/dsp01m613n165k.

MLA Handbook (7^th Edition):

Avanesyan, Levon. “Optimal investment in incomplete markets with multiple Brownian externalities .” 2021. Web. 14 Apr 2021.

Vancouver:

Avanesyan L. Optimal investment in incomplete markets with multiple Brownian externalities . [Internet] [Doctoral dissertation]. Princeton University; 2021. [cited 2021 Apr 14]. Available from: http://arks.princeton.edu/ark:/88435/dsp01m613n165k.

Council of Science Editors:

Avanesyan L. Optimal investment in incomplete markets with multiple Brownian externalities . [Doctoral Dissertation]. Princeton University; 2021. Available from: http://arks.princeton.edu/ark:/88435/dsp01m613n165k

29. Camacho, Frankie. An Inverse-Free Projected Gradient Descent Method for the Generalized Eigenvalue Problem.

Degree: MA, Engineering, 2017, Rice University

URL: http://hdl.handle.net/1911/96001

► The generalized eigenvalue problem is a fundamental numerical linear algebra problem whose applications are wide ranging. For truly large-scale problems, matrices themselves are often not… (more)

Subjects/Keywords: generalized eigenvalue problem; linear algebra; unconstrained optimization

…eigenvalue problem AXk = BXk ⇤k , (1.0.1) where A, B 2 Rn⇥n are symmetric, B is… …eigenpairs for the generalized eigenvalue problem, which we call lobpcg, involves an iterative… …generalized eigenvalue problem–an expensive proposition whenever k becomes a considerable portion of… …One approach for solving the generalized eigenvalue problem that is somewhat similar to 14… …generalized eigenvalue problem, we first recall that in [20] the authors looked to solve…

11 more images…

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Camacho, F. (2017). An Inverse-Free Projected Gradient Descent Method for the Generalized Eigenvalue Problem. (Masters Thesis). Rice University. Retrieved from http://hdl.handle.net/1911/96001

Chicago Manual of Style (16^th Edition):

Camacho, Frankie. “An Inverse-Free Projected Gradient Descent Method for the Generalized Eigenvalue Problem.” 2017. Masters Thesis, Rice University. Accessed April 14, 2021. http://hdl.handle.net/1911/96001.

MLA Handbook (7^th Edition):

Camacho, Frankie. “An Inverse-Free Projected Gradient Descent Method for the Generalized Eigenvalue Problem.” 2017. Web. 14 Apr 2021.

Vancouver:

Camacho F. An Inverse-Free Projected Gradient Descent Method for the Generalized Eigenvalue Problem. [Internet] [Masters thesis]. Rice University; 2017. [cited 2021 Apr 14]. Available from: http://hdl.handle.net/1911/96001.

Council of Science Editors:

Camacho F. An Inverse-Free Projected Gradient Descent Method for the Generalized Eigenvalue Problem. [Masters Thesis]. Rice University; 2017. Available from: http://hdl.handle.net/1911/96001

University of Southern Mississippi

30. Perera, Subagya. Homotopy Analysis Method For Nonlinear Ordinary Eigenvalue Problems.

Degree: MS, 2020, University of Southern Mississippi

URL: https://aquila.usm.edu/masters_theses/720

► In this thesis, we solve nonlinear differential equations by the homotopy analysis method (HAM), which is a semi-analytic method first introduced by Shijun Liao… (more)

Subjects/Keywords: Nonlinear initial value problem; Nonlinear eigenvalue problem; Homotopy analysis method; Duffing's equation; Perturbation theory; Differential Equation.; Ordinary Differential Equations and Applied Dynamics; Other Applied Mathematics; Other Mathematics

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Perera, S. (2020). Homotopy Analysis Method For Nonlinear Ordinary Eigenvalue Problems. (Masters Thesis). University of Southern Mississippi. Retrieved from https://aquila.usm.edu/masters_theses/720

Chicago Manual of Style (16^th Edition):

Perera, Subagya. “Homotopy Analysis Method For Nonlinear Ordinary Eigenvalue Problems.” 2020. Masters Thesis, University of Southern Mississippi. Accessed April 14, 2021. https://aquila.usm.edu/masters_theses/720.

MLA Handbook (7^th Edition):

Perera, Subagya. “Homotopy Analysis Method For Nonlinear Ordinary Eigenvalue Problems.” 2020. Web. 14 Apr 2021.

Vancouver:

Perera S. Homotopy Analysis Method For Nonlinear Ordinary Eigenvalue Problems. [Internet] [Masters thesis]. University of Southern Mississippi; 2020. [cited 2021 Apr 14]. Available from: https://aquila.usm.edu/masters_theses/720.

Council of Science Editors:

Perera S. Homotopy Analysis Method For Nonlinear Ordinary Eigenvalue Problems. [Masters Thesis]. University of Southern Mississippi; 2020. Available from: https://aquila.usm.edu/masters_theses/720

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Open Access Theses and Dissertations