subject:(Eigenvalue)

Kwame Nkrumah University of Science and Technology

1. Kayode, Oladejo Nathaniel. Linear-quadratic optimal control as an inverse eigenvalue problem.

Degree: 2013, Kwame Nkrumah University of Science and Technology

URL: http://dspace.knust.edu.gh:8080/jspui/handle/123456789/9361

►

This thesis investigates Linear-quadratic Control (LQOC)by which is meant a problem in which a linear plant is to be controlled such as to minimize a… (more)

Subjects/Keywords: Linear-Quadratic; Eigenvalue

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APA (6^th Edition):

Kayode, O. N. (2013). Linear-quadratic optimal control as an inverse eigenvalue problem. (Thesis). Kwame Nkrumah University of Science and Technology. Retrieved from http://dspace.knust.edu.gh:8080/jspui/handle/123456789/9361

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):

Kayode, Oladejo Nathaniel. “Linear-quadratic optimal control as an inverse eigenvalue problem.” 2013. Thesis, Kwame Nkrumah University of Science and Technology. Accessed March 30, 2020. http://dspace.knust.edu.gh:8080/jspui/handle/123456789/9361.

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

MLA Handbook (7^th Edition):

Kayode, Oladejo Nathaniel. “Linear-quadratic optimal control as an inverse eigenvalue problem.” 2013. Web. 30 Mar 2020.

Vancouver:

Kayode ON. Linear-quadratic optimal control as an inverse eigenvalue problem. [Internet] [Thesis]. Kwame Nkrumah University of Science and Technology; 2013. [cited 2020 Mar 30]. Available from: http://dspace.knust.edu.gh:8080/jspui/handle/123456789/9361.

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

Council of Science Editors:

Kayode ON. Linear-quadratic optimal control as an inverse eigenvalue problem. [Thesis]. Kwame Nkrumah University of Science and Technology; 2013. Available from: http://dspace.knust.edu.gh:8080/jspui/handle/123456789/9361

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

NSYSU

2. Chen, Chao-Zhong. Optimal upper bounds of eigenvalue ratios for the p-Laplacian.

Degree: Master, Applied Mathematics, 2008, NSYSU

URL: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0819108-160107

► In this thesis, we study the optimal estimate of eigenvalue ratios Î»_n/Î»_m of the Sturm-Liouville equation with Dirichlet boundary conditions on (0, Ï). In 2005,… (more)

Subjects/Keywords: Eigenvalue ratio; Sturm-Liouville equation

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APA (6^th Edition):

Chen, C. (2008). Optimal upper bounds of eigenvalue ratios for the p-Laplacian. (Thesis). NSYSU. Retrieved from http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0819108-160107

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):

Chen, Chao-Zhong. “Optimal upper bounds of eigenvalue ratios for the p-Laplacian.” 2008. Thesis, NSYSU. Accessed March 30, 2020. http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0819108-160107.

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

MLA Handbook (7^th Edition):

Chen, Chao-Zhong. “Optimal upper bounds of eigenvalue ratios for the p-Laplacian.” 2008. Web. 30 Mar 2020.

Vancouver:

Chen C. Optimal upper bounds of eigenvalue ratios for the p-Laplacian. [Internet] [Thesis]. NSYSU; 2008. [cited 2020 Mar 30]. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0819108-160107.

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

Council of Science Editors:

Chen C. Optimal upper bounds of eigenvalue ratios for the p-Laplacian. [Thesis]. NSYSU; 2008. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0819108-160107

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

Penn State University

3. Gill, Daniel Fury. Newton-Krylov Methods for the Solution of the k-Eigenvalue Problem in Multigroup Neutronics Calculations.

Degree: PhD, Nuclear Engineering, 2009, Penn State University

URL: https://etda.libraries.psu.edu/catalog/10162

► In this work we propose using Newton's method, specifically the inexact Newton-GMRES formulation, to solve the k-eigenvalue problem in both transport and diffusion neutronics problems.… (more)

▼ In this work we propose using Newton's method, specifically the inexact Newton-GMRES formulation, to solve the k-eigenvalue problem in both transport and diffusion neutronics problems. This is achieved by choosing a nonlinear function whose roots are the eigenpairs of the k-eigenvalue calculation and then using Newton's method to solve the nonlinear system. The flexibility resulting from the use of a Krylov subspace method to solve the linear Newton step can be further extended via the use of the Jacobian-Free Newton-Krylov (JFNK) approximation, which requires no knowledge of the system's Jacobian; instead only the ability to evaluate the system residual is necessary. This makes it possible to avoid the computational and memory costs associated with the construction and storage of the Jacobian, resulting in an efficient solution algorithm. Writing the k-eigenvalue problem as a nonlinear function yields a number of formulations, all of which all have the desired roots. For the diffusion approximation, the nonlinear function is written in the form of the generalized eigenvalue problem and a set of preconditioners is developed and applied to the GMRES iterations that are used to solve the linearized Newton problem. Most of the developed methods can be implemented as either Newton-Krylov (NK) methods, where the Jacobian-vector product is formed using the explicitly constructed Jacobian, or via the JFNK approximation, where a finite-difference perturbation is used to approximate the Jacobian-vector product. One particularly effective preconditioning option comprises the use of the standard power iteration to precondition the GMRES iteration on either the right or the left. Preconditioning on the left, denoted JFNK(PI), results in a modified nonlinear system whose implementation only requires the ability to perform a single traditional outer iteration, making this approach relatively simple to wrap around an existing diffusion theory k-eigenvalue problem solver. Other preconditioning options, such as the Incomplete Cholesky decomposition of the within-group diffusion matrix, are also considered. Similar methods were developed for transport theory, cast using an operator notation that greatly simplifies their presentation. All of the nonlinear functions developed are written in terms of a generic fixed-point iteration, with a number of specific fixed-point formulations considered. Each fixed-point scheme represents a viable k-eigenvalue problem solution method, with two of the techniques corresponding to traditionally used iterative schemes. The new methods developed can also be wrapped around existing software in most instances, simplifying the implementation process. Ultimately it is seen that the most effective of the Newton formulations in transport theory is wrapped around a k-eigenvalue formulation that is a very special instance of traditional methods: no upscattering iterations are performed, only one inner iteration completed per outer, using source iteration with the previous outer iterate as the initial guess.…

Subjects/Keywords: JFNK; Criticality; Neutron transport; eigenvalue

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APA (6^th Edition):

Gill, D. F. (2009). Newton-Krylov Methods for the Solution of the k-Eigenvalue Problem in Multigroup Neutronics Calculations. (Doctoral Dissertation). Penn State University. Retrieved from https://etda.libraries.psu.edu/catalog/10162

Chicago Manual of Style (16^th Edition):

Gill, Daniel Fury. “Newton-Krylov Methods for the Solution of the k-Eigenvalue Problem in Multigroup Neutronics Calculations.” 2009. Doctoral Dissertation, Penn State University. Accessed March 30, 2020. https://etda.libraries.psu.edu/catalog/10162.

MLA Handbook (7^th Edition):

Gill, Daniel Fury. “Newton-Krylov Methods for the Solution of the k-Eigenvalue Problem in Multigroup Neutronics Calculations.” 2009. Web. 30 Mar 2020.

Vancouver:

Gill DF. Newton-Krylov Methods for the Solution of the k-Eigenvalue Problem in Multigroup Neutronics Calculations. [Internet] [Doctoral dissertation]. Penn State University; 2009. [cited 2020 Mar 30]. Available from: https://etda.libraries.psu.edu/catalog/10162.

Council of Science Editors:

Gill DF. Newton-Krylov Methods for the Solution of the k-Eigenvalue Problem in Multigroup Neutronics Calculations. [Doctoral Dissertation]. Penn State University; 2009. Available from: https://etda.libraries.psu.edu/catalog/10162

Delft University of Technology

4. Li, L. A fundamental study of the Morphological Acceleration Factor:.

Degree: 2010, Delft University of Technology

URL: http://resolver.tudelft.nl/uuid:2780f537-402b-427a-9147-b8652279a83e

► Long-term prediction of sediment transport and morphology has become increasingly important. One of the key issues in carrying out long-term modeling is to bridge the… (more)

Subjects/Keywords: Delft3D; eigenvalue analysis; morphological acceleration

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APA (6^th Edition):

Li, L. (2010). A fundamental study of the Morphological Acceleration Factor:. (Masters Thesis). Delft University of Technology. Retrieved from http://resolver.tudelft.nl/uuid:2780f537-402b-427a-9147-b8652279a83e

Chicago Manual of Style (16^th Edition):

Li, L. “A fundamental study of the Morphological Acceleration Factor:.” 2010. Masters Thesis, Delft University of Technology. Accessed March 30, 2020. http://resolver.tudelft.nl/uuid:2780f537-402b-427a-9147-b8652279a83e.

MLA Handbook (7^th Edition):

Li, L. “A fundamental study of the Morphological Acceleration Factor:.” 2010. Web. 30 Mar 2020.

Vancouver:

Li L. A fundamental study of the Morphological Acceleration Factor:. [Internet] [Masters thesis]. Delft University of Technology; 2010. [cited 2020 Mar 30]. Available from: http://resolver.tudelft.nl/uuid:2780f537-402b-427a-9147-b8652279a83e.

Council of Science Editors:

Li L. A fundamental study of the Morphological Acceleration Factor:. [Masters Thesis]. Delft University of Technology; 2010. Available from: http://resolver.tudelft.nl/uuid:2780f537-402b-427a-9147-b8652279a83e

Baylor University

5. Nelms, Charles F. Eigenvalue comparison theorems for certain boundary value problems and positive solutions for a fifth order singular boundary value problem.

Degree: PhD, Baylor University. Dept. of Mathematics., 2016, Baylor University

URL: http://hdl.handle.net/2104/9631

► Comparison of smallest eigenvalues for certain two point boundary value problems for a fifth order linear differential equation are first obtained. The results are extended… (more)

Subjects/Keywords: Eigenvalue. Comparison. Boundary Value.

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APA (6^th Edition):

Nelms, C. F. (2016). Eigenvalue comparison theorems for certain boundary value problems and positive solutions for a fifth order singular boundary value problem. (Doctoral Dissertation). Baylor University. Retrieved from http://hdl.handle.net/2104/9631

Chicago Manual of Style (16^th Edition):

Nelms, Charles F. “Eigenvalue comparison theorems for certain boundary value problems and positive solutions for a fifth order singular boundary value problem.” 2016. Doctoral Dissertation, Baylor University. Accessed March 30, 2020. http://hdl.handle.net/2104/9631.

MLA Handbook (7^th Edition):

Nelms, Charles F. “Eigenvalue comparison theorems for certain boundary value problems and positive solutions for a fifth order singular boundary value problem.” 2016. Web. 30 Mar 2020.

Vancouver:

Nelms CF. Eigenvalue comparison theorems for certain boundary value problems and positive solutions for a fifth order singular boundary value problem. [Internet] [Doctoral dissertation]. Baylor University; 2016. [cited 2020 Mar 30]. Available from: http://hdl.handle.net/2104/9631.

Council of Science Editors:

Nelms CF. Eigenvalue comparison theorems for certain boundary value problems and positive solutions for a fifth order singular boundary value problem. [Doctoral Dissertation]. Baylor University; 2016. Available from: http://hdl.handle.net/2104/9631

Georgia State University

6. Marsli, Rachid. New Extensions and Applications of Geršgorin Theory.

Degree: PhD, Mathematics and Statistics, 2015, Georgia State University

URL: https://scholarworks.gsu.edu/math_diss/26

► In this work we discover for the first time a strong relationship between Geršgorin theory and the geometric multiplicities of eigenvalues. In fact, if… (more)

Subjects/Keywords: Geršgorin; eigenvalue; geometric multiplicity

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APA (6^th Edition):

Marsli, R. (2015). New Extensions and Applications of Geršgorin Theory. (Doctoral Dissertation). Georgia State University. Retrieved from https://scholarworks.gsu.edu/math_diss/26

Chicago Manual of Style (16^th Edition):

Marsli, Rachid. “New Extensions and Applications of Geršgorin Theory.” 2015. Doctoral Dissertation, Georgia State University. Accessed March 30, 2020. https://scholarworks.gsu.edu/math_diss/26.

MLA Handbook (7^th Edition):

Marsli, Rachid. “New Extensions and Applications of Geršgorin Theory.” 2015. Web. 30 Mar 2020.

Vancouver:

Marsli R. New Extensions and Applications of Geršgorin Theory. [Internet] [Doctoral dissertation]. Georgia State University; 2015. [cited 2020 Mar 30]. Available from: https://scholarworks.gsu.edu/math_diss/26.

Council of Science Editors:

Marsli R. New Extensions and Applications of Geršgorin Theory. [Doctoral Dissertation]. Georgia State University; 2015. Available from: https://scholarworks.gsu.edu/math_diss/26

University of Iowa

7. Landgren, Jeffrey K. An acoustic eigenvalue problem and its application to electrochemistry.

Degree: PhD, Applied Mathematical and Computational Sciences, 2016, University of Iowa

URL: https://ir.uiowa.edu/etd/2104

► The fundamental process that lies at the foundation of batteries, capacitors, and solar cells is the electron transfer process. This takes place at an… (more)

Subjects/Keywords: Eigenvalue; Electrochemistry; Applied Mathematics

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APA (6^th Edition):

Landgren, J. K. (2016). An acoustic eigenvalue problem and its application to electrochemistry. (Doctoral Dissertation). University of Iowa. Retrieved from https://ir.uiowa.edu/etd/2104

Chicago Manual of Style (16^th Edition):

Landgren, Jeffrey K. “An acoustic eigenvalue problem and its application to electrochemistry.” 2016. Doctoral Dissertation, University of Iowa. Accessed March 30, 2020. https://ir.uiowa.edu/etd/2104.

MLA Handbook (7^th Edition):

Landgren, Jeffrey K. “An acoustic eigenvalue problem and its application to electrochemistry.” 2016. Web. 30 Mar 2020.

Vancouver:

Landgren JK. An acoustic eigenvalue problem and its application to electrochemistry. [Internet] [Doctoral dissertation]. University of Iowa; 2016. [cited 2020 Mar 30]. Available from: https://ir.uiowa.edu/etd/2104.

Council of Science Editors:

Landgren JK. An acoustic eigenvalue problem and its application to electrochemistry. [Doctoral Dissertation]. University of Iowa; 2016. Available from: https://ir.uiowa.edu/etd/2104

Iowa State University

8. Luo, Cheng. A comprehensive invariant subspace-based framework for power system small-signal stability analysis.

Degree: 2011, Iowa State University

URL: https://lib.dr.iastate.edu/etd/10109

► With the growth of interconnected power system, and especially the deregulation of the power market, the problems related to small-signal stability have become a critical… (more)

▼ With the growth of interconnected power system, and especially the deregulation of the power market, the problems related to small-signal stability have become a critical issue for the power system security. Better methods of analyzing the oscillations would lead to more accurate determination of these limits and the ability to operate the power system closer to the stability margin. An analytical tool to trace the movement of critical eigenvalues with respect to the changing system conditions will help analyze and investigate the cause of the problem. If the oscillatory stability margin and the damping margin can be pre-determined for a specified scenario which might happen in real time, it could provide operators the user guide in operating the power systems when dealing with the potential oscillation or damping problems. In the dissertation, a novel comprehensive framework of invariant subspace-based methods to deal with the above challenging problems for power system computation and analysis is proposed. We first propose an improved continuation of invariant subspace (ICIS) for the eigenvalue analysis. The ICIS provides us an efficient tool to trace any set of critical eigenvalues of interest. With proper re-initialization, the eigenvalue sensitivities can be successively extracted as by-products of the algorithm during the tracing process. The extracted eigenvalue sensitivity from ICIS is proved mathematically and verified numerically. At each iteration, we not only know the location of each traced eigenvalue, but also the direction and speed of the eigenvalue movement. The extracted eigenvalue sensitivities can be used to automatically adjust the step size in the continuation iteration to improve the efficiency of calculation. From this information, a step size control strategy is proposed to speed up the oscillatory stability margin and damping margin identification. We also propose an improved initialization and update of invariant subspaces, especially for the least damping ratio eigenvalues. The simulation results and computation performance on New England 39-bus system and IEEE 145-bus system are demonstrated in details to show the effectiveness of the algorithm. Results have shown that the ICIS method is an accurate, fast, and robust method in eigenvalue calculation and margin identification. The ICIS provides us an efficient and accurate way to trace a specified subset of eigenvalues of interest for power system small-signal stability analysis, such as rightmost eigenvalues and least damping ratio eigenvalues. It is also a robust method in tracking close or multiple eigenvalues where the conventional methods usually fail to converge. In addition, the ICIS is integrated with the equilibrium point tracing for overall bifurcation analysis in power systems for the identification of voltage stability margin and other eigenvalue-related margins.

Subjects/Keywords: continuation of invariant subspace; critical eigenvalue; damping margin; eigenvalue sensitivity; eigenvalue trajectory; oscillatory stability margin; Electrical and Computer Engineering

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APA (6^th Edition):

Luo, C. (2011). A comprehensive invariant subspace-based framework for power system small-signal stability analysis. (Thesis). Iowa State University. Retrieved from https://lib.dr.iastate.edu/etd/10109

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):

Luo, Cheng. “A comprehensive invariant subspace-based framework for power system small-signal stability analysis.” 2011. Thesis, Iowa State University. Accessed March 30, 2020. https://lib.dr.iastate.edu/etd/10109.

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

MLA Handbook (7^th Edition):

Luo, Cheng. “A comprehensive invariant subspace-based framework for power system small-signal stability analysis.” 2011. Web. 30 Mar 2020.

Vancouver:

Luo C. A comprehensive invariant subspace-based framework for power system small-signal stability analysis. [Internet] [Thesis]. Iowa State University; 2011. [cited 2020 Mar 30]. Available from: https://lib.dr.iastate.edu/etd/10109.

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

Council of Science Editors:

Luo C. A comprehensive invariant subspace-based framework for power system small-signal stability analysis. [Thesis]. Iowa State University; 2011. Available from: https://lib.dr.iastate.edu/etd/10109

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

North Carolina State University

9. Liu, Ning. Spectral Clustering for Graphs and Markov Chains.

Degree: PhD, Computer Science, 2010, North Carolina State University

URL: http://www.lib.ncsu.edu/resolver/1840.16/4886

► Spectral graph partitioning based on spectral theory has become a popular clustering method over the last few years. The starting point is the work of… (more)

▼ Spectral graph partitioning based on spectral theory has become a popular clustering method over the last few years. The starting point is the work of Fiedler who shows that an eigenvector of the Laplacian matrix of an undirected graph (symmetric system) provides the minimum cut of graph nodes. The spectral technique can also be applied to a Markov chain to cluster states and, in general, is more broadly applicable to nonsymmetric systems. Enlightened by these facts, we combine them to show that Markov chains, due to two different clustering techniques they offer, are effective approaches for clustering in more general situations. In this dissertation, we advance the state of the art of spectral clustering and introduce a new algorithm to decompose matrices into blocks. We first prove that the second eigenvector of the signless Laplacian provides a heuristic solution to the NP-complete state clustering problem which is the dual problem of graph partitioning. A new method for clustering nodes of a graph that have negative edge weights is also proposed. Second, a connection between the singular vectors obtained from an SVD decomposition and the eigenvectors from spectral algorithms on data clustering is revealed. We show that the singular vectors of the node-edge incidence matrix generate not only clusters on the nodes but also clusters on the edges. Third, relating spectral clustering and state clustering of Markov chains, we present two clustering techniques for Markov chains based on two different measures and suggest a mean of incorporating both techniques to obtain comprehensive information concerning state clusters. Fourth, we display the connection between spectral clustering and dimension reduction techniques in statistical clustering. Also, the results obtained from spectral and statistical clustering are shown to be related. Finally, we develop a new improved spectral clustering procedure for decomposing matrices into blocks. This algorithm works well in several applications, especially in problems of detecting communities in complex networks, where some existing methods, e.g. MARCA and TPABLO, fail. Advisors/Committee Members: Dr. William J. Stewart, Committee Chair (advisor), Dr. Harry G. Perros, Committee Co-Chair (advisor), Dr. Laurie Williams, Committee Member (advisor), Dr. Michael Devetsikiotis, Committee Member (advisor).

Subjects/Keywords: spectral clustering; graph partitioning; markov chains; eigenvalue

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APA (6^th Edition):

Liu, N. (2010). Spectral Clustering for Graphs and Markov Chains. (Doctoral Dissertation). North Carolina State University. Retrieved from http://www.lib.ncsu.edu/resolver/1840.16/4886

Chicago Manual of Style (16^th Edition):

Liu, Ning. “Spectral Clustering for Graphs and Markov Chains.” 2010. Doctoral Dissertation, North Carolina State University. Accessed March 30, 2020. http://www.lib.ncsu.edu/resolver/1840.16/4886.

MLA Handbook (7^th Edition):

Liu, Ning. “Spectral Clustering for Graphs and Markov Chains.” 2010. Web. 30 Mar 2020.

Vancouver:

Liu N. Spectral Clustering for Graphs and Markov Chains. [Internet] [Doctoral dissertation]. North Carolina State University; 2010. [cited 2020 Mar 30]. Available from: http://www.lib.ncsu.edu/resolver/1840.16/4886.

Council of Science Editors:

Liu N. Spectral Clustering for Graphs and Markov Chains. [Doctoral Dissertation]. North Carolina State University; 2010. Available from: http://www.lib.ncsu.edu/resolver/1840.16/4886

NSYSU

10. 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 March 30, 2020. 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. 30 Mar 2020.

Vancouver:

Chang H. The End Game Problem in Solving Algebraic Eigenvalue Problems by Homotopy Continuation Method. [Internet] [Thesis]. NSYSU; 2013. [cited 2020 Mar 30]. 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

NSYSU

11. Fu, Wen-Chuan. The Evolution of Mass Species under the Replicator Equation.

Degree: Master, Physics, 2014, NSYSU

URL: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0516114-205812

► We study the evolutionary of species under the replicator equation with antisymmetric payoff . All of out results show odd number of species survived and… (more)

Subjects/Keywords: Replicator Equation; Game Theory; eigenvalue; Payoff

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APA (6^th Edition):

Fu, W. (2014). The Evolution of Mass Species under the Replicator Equation. (Thesis). NSYSU. Retrieved from http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0516114-205812

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):

Fu, Wen-Chuan. “The Evolution of Mass Species under the Replicator Equation.” 2014. Thesis, NSYSU. Accessed March 30, 2020. http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0516114-205812.

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

MLA Handbook (7^th Edition):

Fu, Wen-Chuan. “The Evolution of Mass Species under the Replicator Equation.” 2014. Web. 30 Mar 2020.

Vancouver:

Fu W. The Evolution of Mass Species under the Replicator Equation. [Internet] [Thesis]. NSYSU; 2014. [cited 2020 Mar 30]. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0516114-205812.

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

Council of Science Editors:

Fu W. The Evolution of Mass Species under the Replicator Equation. [Thesis]. NSYSU; 2014. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0516114-205812

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

NSYSU

12. Huang, Hsien-kuei. Optimal estimates of the eigenvalue gap and eigenvalue ratio with variational.

Degree: Master, Applied Mathematics, 2004, NSYSU

URL: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0911104-022942

► The optimal estimates of the eigenvalue gaps and eigenvalue ratios for the Sturm-Liouville operators have been of fundamental importance. Recently a series of works by… (more)

Subjects/Keywords: optimal estimates; eigenvalue

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APA (6^th Edition):

Huang, H. (2004). Optimal estimates of the eigenvalue gap and eigenvalue ratio with variational. (Thesis). NSYSU. Retrieved from http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0911104-022942

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):

Huang, Hsien-kuei. “Optimal estimates of the eigenvalue gap and eigenvalue ratio with variational.” 2004. Thesis, NSYSU. Accessed March 30, 2020. http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0911104-022942.

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

MLA Handbook (7^th Edition):

Huang, Hsien-kuei. “Optimal estimates of the eigenvalue gap and eigenvalue ratio with variational.” 2004. Web. 30 Mar 2020.

Vancouver:

Huang H. Optimal estimates of the eigenvalue gap and eigenvalue ratio with variational. [Internet] [Thesis]. NSYSU; 2004. [cited 2020 Mar 30]. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0911104-022942.

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

Council of Science Editors:

Huang H. Optimal estimates of the eigenvalue gap and eigenvalue ratio with variational. [Thesis]. NSYSU; 2004. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0911104-022942

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

NSYSU

13. Kung, Shing-Yuan. Density functions with extremal antiperiodic eigenvalues and related topics.

Degree: Master, Applied Mathematics, 2005, NSYSU

URL: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0122105-211845

► In this thesis, we prove 2 theorems. First let Ï0 be a minimizing (or maximizing) density function for the first antiperiodic eigenvalue Î»1' in E[h,H,M],… (more)

Subjects/Keywords: Density functions; eigenvalue

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

APA (6^th Edition):

Kung, S. (2005). Density functions with extremal antiperiodic eigenvalues and related topics. (Thesis). NSYSU. Retrieved from http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0122105-211845

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):

Kung, Shing-Yuan. “Density functions with extremal antiperiodic eigenvalues and related topics.” 2005. Thesis, NSYSU. Accessed March 30, 2020. http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0122105-211845.

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

MLA Handbook (7^th Edition):

Kung, Shing-Yuan. “Density functions with extremal antiperiodic eigenvalues and related topics.” 2005. Web. 30 Mar 2020.

Vancouver:

Kung S. Density functions with extremal antiperiodic eigenvalues and related topics. [Internet] [Thesis]. NSYSU; 2005. [cited 2020 Mar 30]. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0122105-211845.

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

Council of Science Editors:

Kung S. Density functions with extremal antiperiodic eigenvalues and related topics. [Thesis]. NSYSU; 2005. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0122105-211845

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

NSYSU

14. Chan, Yu-Lin. A Numerical Method to Solve the Divergence Issue of Microwave Circuit Model Extraction.

Degree: Master, Electrical Engineering, 2012, NSYSU

URL: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0808112-141533

► With the development of consumer electronics, the circuitry structure become more complex, For this reason, it might cause numerical errors to be cumulated in the… (more)

Subjects/Keywords: Singular Value; Eigenvalue; Causality; Passivity; Hilbert Transform

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

APA (6^th Edition):

Chan, Y. (2012). A Numerical Method to Solve the Divergence Issue of Microwave Circuit Model Extraction. (Thesis). NSYSU. Retrieved from http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0808112-141533

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):

Chan, Yu-Lin. “A Numerical Method to Solve the Divergence Issue of Microwave Circuit Model Extraction.” 2012. Thesis, NSYSU. Accessed March 30, 2020. http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0808112-141533.

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

MLA Handbook (7^th Edition):

Chan, Yu-Lin. “A Numerical Method to Solve the Divergence Issue of Microwave Circuit Model Extraction.” 2012. Web. 30 Mar 2020.

Vancouver:

Chan Y. A Numerical Method to Solve the Divergence Issue of Microwave Circuit Model Extraction. [Internet] [Thesis]. NSYSU; 2012. [cited 2020 Mar 30]. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0808112-141533.

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

Council of Science Editors:

Chan Y. A Numerical Method to Solve the Divergence Issue of Microwave Circuit Model Extraction. [Thesis]. NSYSU; 2012. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0808112-141533

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

Universiteit Utrecht

15. Rommes, J. Methods for eigenvalue problems with applications in model order reduction.

Degree: 2007, Universiteit Utrecht

URL: http://dspace.library.uu.nl:8080/handle/1874/21787

► Physical structures and processes are modeled by dynamical systems in a wide range of application areas. The increasing demand for complex components and large structures,… (more)

▼ Physical structures and processes are modeled by dynamical systems in a wide range of application areas. The increasing demand for complex components and large structures, together with an increasing demand for detail and accuracy, makes the models larger and more complicated. To be able to simulate these large-scale systems, there is need for reduced-order models of much smaller size, that approximate the behavior of the original model and preserve the important characteristics. In this thesis, algorithms are presented that compute the important characteristics and construct reduced-order models. The eigenvalue problems related to these large-scale dynamical systems are usually too large to be solved completely. The algorithms described in this thesis are efficient and effective methods for the computation of specific dominant eigenvalues. Here, the interpretation of the adjective dominant depends on the application from which the eigenproblem arises. In stability analysis, one is interested in the rightmost eigenvalues, while in other applications the dominant eigenvalues are the natural frequencies. For general linear time invariant dynamical systems, the dominant eigenvalues are the poles of the transfer function that contribute significantly to the frequency response. Many of the methods are based on Newton's method and are similar to (two-sided) Rayleigh quotient iteration. It is shown that compared to (two-sided) Rayleigh quotient iteration, the new methods, Subspace Accelerated Dominant Pole Algorithm (SADPA) and Subspace Accelerated MIMO Dominant Pole Algorithm (SAMDP), have better convergence to the dominant poles of SISO and MIMO transfer functions, respectively. Because SADPA and SAMDP take advantage of efficient deflation for the computation of more than one dominant pole and compute the dominant poles automatically, they are preferred over (two-sided) Jacobi-Davidson methods and Arnoldi based methods. SADPA and SAMDP can be generalized to methods for the computation of dominant transfer function zeros and dominant poles of higher-order transfer functions. The computed eigenvalues and corresponding eigenvectors can be used to construct reduced-order models in the form of modal approximations, but also to improve reduced-order models computed by Krylov subspace based techniques. Large-scale generalized eigenvalue problems arise, for instance, in stability analysis of discretized Navier-Stokes equations and other systems. Due to singularity of one of the matrices in the pencil, there may be eigenvalues at infinity. These eigenvalues at infinity have no physical relevance, but their presence complicates the computation of the rightmost finite eigenvalues. Standard Arnoldi and Jacobi-Davidson approaches may fail because they may interpret approximations of eigenvalues at infinity as approximations to finite eigenvalues. New strategies that combine shift-and-invert and Cayley transformations with purification techniques, and exploit the structure of the eigenvalue problem, are presented to compute the…

Subjects/Keywords: Wiskunde en Informatica; eigenvalue problems; model order reduction; eigenvalue methods; modal approximation; dominant poles; generalized eigenvalue problems; quadratic eigenvalue problems; purification; Jacobi-Davidson method; two-sided Rayleigh quotient iteration

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APA (6^th Edition):

Rommes, J. (2007). Methods for eigenvalue problems with applications in model order reduction. (Doctoral Dissertation). Universiteit Utrecht. Retrieved from http://dspace.library.uu.nl:8080/handle/1874/21787

Chicago Manual of Style (16^th Edition):

Rommes, J. “Methods for eigenvalue problems with applications in model order reduction.” 2007. Doctoral Dissertation, Universiteit Utrecht. Accessed March 30, 2020. http://dspace.library.uu.nl:8080/handle/1874/21787.

MLA Handbook (7^th Edition):

Rommes, J. “Methods for eigenvalue problems with applications in model order reduction.” 2007. Web. 30 Mar 2020.

Vancouver:

Rommes J. Methods for eigenvalue problems with applications in model order reduction. [Internet] [Doctoral dissertation]. Universiteit Utrecht; 2007. [cited 2020 Mar 30]. Available from: http://dspace.library.uu.nl:8080/handle/1874/21787.

Council of Science Editors:

Rommes J. Methods for eigenvalue problems with applications in model order reduction. [Doctoral Dissertation]. Universiteit Utrecht; 2007. Available from: http://dspace.library.uu.nl:8080/handle/1874/21787

University of Arkansas

16. Hutchison, Brandon. A Restarted Homotopy Method for the Nonsymmetric Eigenvalue Problem.

Degree: PhD, 2011, University of Arkansas

URL: https://scholarworks.uark.edu/etd/74

► The eigenvalues and eigenvectors of a Hessenberg matrix, H, are computed with a combination of homotopy increments and the Arnoldi method. Given a set,… (more)

Subjects/Keywords: Arnoldi; Continuation; Eigenvalue; Homotopy; Applied Mathematics

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

APA (6^th Edition):

Hutchison, B. (2011). A Restarted Homotopy Method for the Nonsymmetric Eigenvalue Problem. (Doctoral Dissertation). University of Arkansas. Retrieved from https://scholarworks.uark.edu/etd/74

Chicago Manual of Style (16^th Edition):

Hutchison, Brandon. “A Restarted Homotopy Method for the Nonsymmetric Eigenvalue Problem.” 2011. Doctoral Dissertation, University of Arkansas. Accessed March 30, 2020. https://scholarworks.uark.edu/etd/74.

MLA Handbook (7^th Edition):

Hutchison, Brandon. “A Restarted Homotopy Method for the Nonsymmetric Eigenvalue Problem.” 2011. Web. 30 Mar 2020.

Vancouver:

Hutchison B. A Restarted Homotopy Method for the Nonsymmetric Eigenvalue Problem. [Internet] [Doctoral dissertation]. University of Arkansas; 2011. [cited 2020 Mar 30]. Available from: https://scholarworks.uark.edu/etd/74.

Council of Science Editors:

Hutchison B. A Restarted Homotopy Method for the Nonsymmetric Eigenvalue Problem. [Doctoral Dissertation]. University of Arkansas; 2011. Available from: https://scholarworks.uark.edu/etd/74

University of Arizona

17. Fox, Matthew Kins. Spectrum of Hamiltonian Matrices .

Degree: 2018, University of Arizona

URL: http://hdl.handle.net/10150/628423

► Random Hamiltonian Matrices are a Lie Algebra that can be connected to approximations of random Hamiltonian systems near equilibria. In Alan Edelman’s paper, he was… (more)

Subjects/Keywords: Density; Eigenvalue; Ginibre; Hamiltonian; Probability; Spectrum

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APA (6^th Edition):

Fox, M. K. (2018). Spectrum of Hamiltonian Matrices . (Doctoral Dissertation). University of Arizona. Retrieved from http://hdl.handle.net/10150/628423

Chicago Manual of Style (16^th Edition):

Fox, Matthew Kins. “Spectrum of Hamiltonian Matrices .” 2018. Doctoral Dissertation, University of Arizona. Accessed March 30, 2020. http://hdl.handle.net/10150/628423.

MLA Handbook (7^th Edition):

Fox, Matthew Kins. “Spectrum of Hamiltonian Matrices .” 2018. Web. 30 Mar 2020.

Vancouver:

Fox MK. Spectrum of Hamiltonian Matrices . [Internet] [Doctoral dissertation]. University of Arizona; 2018. [cited 2020 Mar 30]. Available from: http://hdl.handle.net/10150/628423.

Council of Science Editors:

Fox MK. Spectrum of Hamiltonian Matrices . [Doctoral Dissertation]. University of Arizona; 2018. Available from: http://hdl.handle.net/10150/628423

University of Waterloo

18. Wang, Ningchuan. Eigenvalue, Quadratic Programming and Semidefinite Programming Bounds for Graph Partitioning Problems.

Degree: 2014, University of Waterloo

URL: http://hdl.handle.net/10012/8760

► The Graph Partitioning problems are hard combinatorial optimization problems. We are interested in both lower bounds and upper bounds. We introduce several methods including basic… (more)

Subjects/Keywords: Graph Partitioning; Semidefinite Programming; eigenvalue bounds

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APA (6^th Edition):

Wang, N. (2014). Eigenvalue, Quadratic Programming and Semidefinite Programming Bounds for Graph Partitioning Problems. (Thesis). University of Waterloo. Retrieved from http://hdl.handle.net/10012/8760

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):

Wang, Ningchuan. “Eigenvalue, Quadratic Programming and Semidefinite Programming Bounds for Graph Partitioning Problems.” 2014. Thesis, University of Waterloo. Accessed March 30, 2020. http://hdl.handle.net/10012/8760.

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

MLA Handbook (7^th Edition):

Wang, Ningchuan. “Eigenvalue, Quadratic Programming and Semidefinite Programming Bounds for Graph Partitioning Problems.” 2014. Web. 30 Mar 2020.

Vancouver:

Wang N. Eigenvalue, Quadratic Programming and Semidefinite Programming Bounds for Graph Partitioning Problems. [Internet] [Thesis]. University of Waterloo; 2014. [cited 2020 Mar 30]. Available from: http://hdl.handle.net/10012/8760.

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

Council of Science Editors:

Wang N. Eigenvalue, Quadratic Programming and Semidefinite Programming Bounds for Graph Partitioning Problems. [Thesis]. University of Waterloo; 2014. Available from: http://hdl.handle.net/10012/8760

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

Universitat Politècnica de València

19. Romero Alcalde, Eloy. Parallel implementation of Davidson-type methods for large-scale eigenvalue problems .

Degree: 2012, Universitat Politècnica de València

URL: http://hdl.handle.net/10251/15188

► El problema de valores propios (tambien llamado de autovalores, o eigenvalues) esta presente en diversas tareas cienficas a traves de la resolucion de ecuaciones diferenciales,… (more)

▼ El problema de valores propios (tambien llamado de autovalores, o eigenvalues) esta presente en diversas tareas cienficas a traves de la resolucion de ecuaciones diferenciales, analisis de modelos y calculos de funciones matriciales, entre otras muchas aplicaciones. Si los problemas son de dimension moderada (menor a 106), pueden ser abordados mediante los llamados metodos directos, como el algoritmo iterativo QR o el metodo de divide y vencerlas. Sin embargo, si el problema es de gran dimension y solo se requieren unas pocas soluciones (comparado con el tama~no del problema) y con un cierto grado de aproximacion, los metodos iterativos pueden resultar mas eficientes. Ademas los metodos iterativos pueden ofrecer mejores prestaciones en arquitecturas de altas prestaciones, como las de memoria distribuida, en las que existen un cierto numero de nodos computacionales con espacio de memoria propios y solo pueden compartir informacion y sincronizarse mediante el paso de mensajes. Esta tesis aborda la implementacion de metodos de tipo Davidson, destacando Generalized Davidson y Jacobi-Davidson, una clase de metodos iterativos que puede ser competitiva en casos especialmente dificiles como calcular valores propios en el interior del espectro o cuando la factorizacion de matrices es prohibitiva o ineficiente, y solo es posible una factorizacion aproximada. La implementacion se desarrolla en SLEPc (Scalable Library for Eigenvalue Problem Computations), libreria libre destacada en la resolucion de problemas de gran tama~no de valores propios, problemas cuadraticos de valores propios y problemas de valores singulares, entre otros. A su vez, SLEPc se desarrolla bajo el marco de PETSc (Portable, Extensible Toolkit for Scientic Computation), que ofrece implementaciones eficientes de operaciones basicas del algebra lineal, como operaciones con matrices y vectores, resolucion aproximada de sistemas lineales, factorizaciones exactas y aproximadas de matrices, etc. Advisors/Committee Members: Román Moltó, José Enrique (advisor).

Subjects/Keywords: Eigenvalue problems; Davidson methods; Distributed computing

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

APA (6^th Edition):

Romero Alcalde, E. (2012). Parallel implementation of Davidson-type methods for large-scale eigenvalue problems . (Doctoral Dissertation). Universitat Politècnica de València. Retrieved from http://hdl.handle.net/10251/15188

Chicago Manual of Style (16^th Edition):

Romero Alcalde, Eloy. “Parallel implementation of Davidson-type methods for large-scale eigenvalue problems .” 2012. Doctoral Dissertation, Universitat Politècnica de València. Accessed March 30, 2020. http://hdl.handle.net/10251/15188.

MLA Handbook (7^th Edition):

Romero Alcalde, Eloy. “Parallel implementation of Davidson-type methods for large-scale eigenvalue problems .” 2012. Web. 30 Mar 2020.

Vancouver:

Romero Alcalde E. Parallel implementation of Davidson-type methods for large-scale eigenvalue problems . [Internet] [Doctoral dissertation]. Universitat Politècnica de València; 2012. [cited 2020 Mar 30]. Available from: http://hdl.handle.net/10251/15188.

Council of Science Editors:

Romero Alcalde E. Parallel implementation of Davidson-type methods for large-scale eigenvalue problems . [Doctoral Dissertation]. Universitat Politècnica de València; 2012. Available from: http://hdl.handle.net/10251/15188

Baylor University

20. Neugebauer, Jeffrey T. Comparison of smallest eigenvalues and extremal points for third and fourth order three point boundary value problems.

Degree: PhD, Mathematics., 2011, Baylor University

URL: http://hdl.handle.net/2104/8235

► The theory of u₀-positive operators with respect to a cone in a Banach space is applied to the linear differential equations u⁽⁴⁾ + λ₁p(x)u =… (more)

Subjects/Keywords: Differential equations.; Eigenvalue problems.; Extremal points.

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APA (6^th Edition):

Neugebauer, J. T. (2011). Comparison of smallest eigenvalues and extremal points for third and fourth order three point boundary value problems. (Doctoral Dissertation). Baylor University. Retrieved from http://hdl.handle.net/2104/8235

Chicago Manual of Style (16^th Edition):

Neugebauer, Jeffrey T. “Comparison of smallest eigenvalues and extremal points for third and fourth order three point boundary value problems.” 2011. Doctoral Dissertation, Baylor University. Accessed March 30, 2020. http://hdl.handle.net/2104/8235.

MLA Handbook (7^th Edition):

Neugebauer, Jeffrey T. “Comparison of smallest eigenvalues and extremal points for third and fourth order three point boundary value problems.” 2011. Web. 30 Mar 2020.

Vancouver:

Neugebauer JT. Comparison of smallest eigenvalues and extremal points for third and fourth order three point boundary value problems. [Internet] [Doctoral dissertation]. Baylor University; 2011. [cited 2020 Mar 30]. Available from: http://hdl.handle.net/2104/8235.

Council of Science Editors:

Neugebauer JT. Comparison of smallest eigenvalues and extremal points for third and fourth order three point boundary value problems. [Doctoral Dissertation]. Baylor University; 2011. Available from: http://hdl.handle.net/2104/8235

University of Minnesota

21. Kakade, Virendra Vilas. Eigenvalue based alternans prediction and the effects of heart rate variability on alternans formation.

Degree: MS, Electrical Engineering, 2013, University of Minnesota

URL: http://hdl.handle.net/11299/165538

► Ventricular fibrillation, a leading cause of death in the US, is an instability observed at the whole heart level which may result from the alternation… (more)

▼ Ventricular fibrillation, a leading cause of death in the US, is an instability observed at the whole heart level which may result from the alternation of action potential viz. alternans at the cellular level. Previous approaches to predict alternans formation are based on the slope of the restitution curve which is the relation between the action potential duration (APD) and the duration of the preceding diastolic interval (DI). These approaches propose that alternans exists when the slope of this curve is greater than one and ceases to exist otherwise. However restitution based approaches have not been successful in all cases. One of the shortcomings of restitution approach is the non-uniqueness of the restitution curve which results from the variety of pacing protocols used to construct it. This has lead to observations in which alternans existed when the slope was less than one and vice a versa. Moreover restitution approaches use just one measurement from each action potential(AP). Another shortcoming of these approaches is periodic pacing, which is employed to attain the responses (APD and DI) at different basic cycle lengths (BCL) to construct the restitution curve. Upon analysis of electrocardiograms, it is evident that natural pacing is not periodic and exhibits rate variability which can be seen from measurement of RR intervals (which are analogous to BCL) over time. It would be beneficial to develop a method which is not very related to the restitution approach to predict alternans formation and which would not necessitate the generation of a curve and thus reduce errors introduced due to slope calculation. Such a method could also use multiple measurements from each AP to characterize it. Also, it would be beneficial to study the effects of introducing variability in pacing, on alternans formation. Analysis of such data would give us some valuable insight into the complex phenomenon of alternans. With these two shortcomings in sight two studies were conducted with specific aims as follows:Aim1: Apply a dominant eigenvalue method to predict alternans formation in the rabbit heart. A dominant eigenvalue based alternans prediction was recently developed and tested on data obtained from single cell numerical simulation data. I applied this technique at whole heart level to test whether alternans formation could be predicted using a eigenvalue calculated at each BCL from AP response data. I found that the eigenvalue showed decreasing trend towards the value of -1 as BCL was decreased and approached alternans onset. Aim2: Study the effect of introducing rate variability in pacing on a ionic model of a single cell. Ionic model of a single cell was paced using two protocols which introduced variability in the pacing rate by either varying the BCL or DI to test the effects on alternans formation. It was found that introducing variability using first method (varying BCL) lead to alternans formation over wider range of BCL than without variability. The second method (varying DI) however did not give rise to…

Subjects/Keywords: Alternans; Eigenvalue; Heart; Heart rate variability

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APA (6^th Edition):

Kakade, V. V. (2013). Eigenvalue based alternans prediction and the effects of heart rate variability on alternans formation. (Masters Thesis). University of Minnesota. Retrieved from http://hdl.handle.net/11299/165538

Chicago Manual of Style (16^th Edition):

Kakade, Virendra Vilas. “Eigenvalue based alternans prediction and the effects of heart rate variability on alternans formation.” 2013. Masters Thesis, University of Minnesota. Accessed March 30, 2020. http://hdl.handle.net/11299/165538.

MLA Handbook (7^th Edition):

Kakade, Virendra Vilas. “Eigenvalue based alternans prediction and the effects of heart rate variability on alternans formation.” 2013. Web. 30 Mar 2020.

Vancouver:

Kakade VV. Eigenvalue based alternans prediction and the effects of heart rate variability on alternans formation. [Internet] [Masters thesis]. University of Minnesota; 2013. [cited 2020 Mar 30]. Available from: http://hdl.handle.net/11299/165538.

Council of Science Editors:

Kakade VV. Eigenvalue based alternans prediction and the effects of heart rate variability on alternans formation. [Masters Thesis]. University of Minnesota; 2013. Available from: http://hdl.handle.net/11299/165538

University of New Mexico

22. Myers, Nicholas. An Sn Application of Homotopy Continuation in Neutral Particle Transport.

Degree: Nuclear Engineering, 2014, University of New Mexico

URL: http://hdl.handle.net/1928/24581

► The objective of this dissertation is to investigate the usefulness of homotopy continuation applied in the context of neutral particle transport where traditional methods of… (more)

Subjects/Keywords: Homotopy; Sn; Continuation; Transport; Eigenvalue; Diffusive

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APA (6^th Edition):

Myers, N. (2014). An Sn Application of Homotopy Continuation in Neutral Particle Transport. (Doctoral Dissertation). University of New Mexico. Retrieved from http://hdl.handle.net/1928/24581

Chicago Manual of Style (16^th Edition):

Myers, Nicholas. “An Sn Application of Homotopy Continuation in Neutral Particle Transport.” 2014. Doctoral Dissertation, University of New Mexico. Accessed March 30, 2020. http://hdl.handle.net/1928/24581.

MLA Handbook (7^th Edition):

Myers, Nicholas. “An Sn Application of Homotopy Continuation in Neutral Particle Transport.” 2014. Web. 30 Mar 2020.

Vancouver:

Myers N. An Sn Application of Homotopy Continuation in Neutral Particle Transport. [Internet] [Doctoral dissertation]. University of New Mexico; 2014. [cited 2020 Mar 30]. Available from: http://hdl.handle.net/1928/24581.

Council of Science Editors:

Myers N. An Sn Application of Homotopy Continuation in Neutral Particle Transport. [Doctoral Dissertation]. University of New Mexico; 2014. Available from: http://hdl.handle.net/1928/24581

University of Ontario Institute of Technology

23. Lee, Eungkil. Design optimization of active trailer differential braking systems for car-trailer combinations.

Degree: 2016, University of Ontario Institute of Technology

URL: http://hdl.handle.net/10155/701

► The thesis studies active trailer differential braking (ATDB) systems to improve the lateral stability of car-trailer (CT) combinations. CT combinations exhibit unique unstable motion modes,… (more)

Subjects/Keywords: ATDB; Genetic algorithm; LQR; Mu synthesis; Eigenvalue

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APA (6^th Edition):

Lee, E. (2016). Design optimization of active trailer differential braking systems for car-trailer combinations. (Thesis). University of Ontario Institute of Technology. Retrieved from http://hdl.handle.net/10155/701

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, Eungkil. “Design optimization of active trailer differential braking systems for car-trailer combinations.” 2016. Thesis, University of Ontario Institute of Technology. Accessed March 30, 2020. http://hdl.handle.net/10155/701.

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, Eungkil. “Design optimization of active trailer differential braking systems for car-trailer combinations.” 2016. Web. 30 Mar 2020.

Vancouver:

Lee E. Design optimization of active trailer differential braking systems for car-trailer combinations. [Internet] [Thesis]. University of Ontario Institute of Technology; 2016. [cited 2020 Mar 30]. Available from: http://hdl.handle.net/10155/701.

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

Council of Science Editors:

Lee E. Design optimization of active trailer differential braking systems for car-trailer combinations. [Thesis]. University of Ontario Institute of Technology; 2016. Available from: http://hdl.handle.net/10155/701

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

Wayne State University

24. Hu, Jiaxi. Shape Analysis Using Spectral Geometry.

Degree: PhD, Computer Science, 2015, Wayne State University

URL: https://digitalcommons.wayne.edu/oa_dissertations/1143

► Shape analysis is a fundamental research topic in computer graphics and computer vision. To date, more and more 3D data is produced by those… (more)

▼ Shape analysis is a fundamental research topic in computer graphics and computer vision. To date, more and more 3D data is produced by those advanced acquisition capture devices, e.g., laser scanners, depth cameras, and CT/MRI scanners. The increasing data demands advanced analysis tools including shape matching, retrieval, deformation, etc. Nevertheless, 3D Shapes are represented with Euclidean transformations such as translation, scaling, and rotation and digital mesh representations are irregularly sampled. The shape can also deform non-linearly and the sampling may vary. In order to address these challenging problems, we investigate Laplace-Beltrami shape spectra from the differential geometry perspective, focusing more on the intrinsic properties. In this dissertation, the shapes are represented with 2 manifolds, which are differentiable. First, we discuss in detail about the salient geometric feature points in the Laplace-Beltrami spectral domain instead of traditional spatial domains. Simultaneously, the local shape descriptor of a feature point is the Laplace-Beltrami spectrum of the spatial region associated to the point, which are stable and distinctive. The salient spectral geometric features are invariant to spatial Euclidean transforms, isometric deformations and mesh triangulations. Both global and partial matching can be achieved with these salient feature points. Next, we introduce a novel method to analyze a set of poses, i.e., near-isometric deformations, of 3D models that are unregistered. Different shapes of poses are transformed from the 3D spatial domain to a geometry spectral one where all near isometric deformations, mesh triangulations and Euclidean transformations are filtered away. Semantic parts of that model are then determined based on the computed geometric properties of all the mapped vertices in the geometry spectral domain while semantic skeleton can be automatically built with joints detected. Finally we prove the shape spectrum is a continuous function to a scale function on the conformal factor of the manifold. The derivatives of the eigenvalues are analytically expressed with those of the scale function. The property applies to both continuous domain and discrete triangle meshes. On the triangle meshes, a spectrum alignment algorithm is developed. Given two closed triangle meshes, the eigenvalues can be aligned from one to the other and the eigenfunction distributions are aligned as well. This extends the shape spectra across non-isometric deformations, supporting a registration-free analysis of general motion data. Advisors/Committee Members: Jing Hu.

Subjects/Keywords: eigenfunction; eigenvalue; eigenvalue variation; shape analysis; shape spectrum; spectral geometry; Computer Sciences

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APA (6^th Edition):

Hu, J. (2015). Shape Analysis Using Spectral Geometry. (Doctoral Dissertation). Wayne State University. Retrieved from https://digitalcommons.wayne.edu/oa_dissertations/1143

Chicago Manual of Style (16^th Edition):

Hu, Jiaxi. “Shape Analysis Using Spectral Geometry.” 2015. Doctoral Dissertation, Wayne State University. Accessed March 30, 2020. https://digitalcommons.wayne.edu/oa_dissertations/1143.

MLA Handbook (7^th Edition):

Hu, Jiaxi. “Shape Analysis Using Spectral Geometry.” 2015. Web. 30 Mar 2020.

Vancouver:

Hu J. Shape Analysis Using Spectral Geometry. [Internet] [Doctoral dissertation]. Wayne State University; 2015. [cited 2020 Mar 30]. Available from: https://digitalcommons.wayne.edu/oa_dissertations/1143.

Council of Science Editors:

Hu J. Shape Analysis Using Spectral Geometry. [Doctoral Dissertation]. Wayne State University; 2015. Available from: https://digitalcommons.wayne.edu/oa_dissertations/1143

Wright State University

25. 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 ¿ of a typical quadratic eigenvalue problem (QEP). Indeed, solutions ¿ 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 · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

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 March 30, 2020. 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. 30 Mar 2020.

Vancouver:

Ali AH. Modifying Some Iterative Methods for Solving Quadratic Eigenvalue Problems. [Internet] [Masters thesis]. Wright State University; 2017. [cited 2020 Mar 30]. 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

University of Houston

26. Nyberg, Amy 1975-. The Laplacian Spectra of Random Geometric Graphs.

Degree: PhD, Physics, 2014, University of Houston

URL: http://hdl.handle.net/10657/1646

► In this dissertation we study a problem in mathematical physics concerning the eigenvalues of random matrices. A network may be represented by any of several… (more)

▼ In this dissertation we study a problem in mathematical physics concerning the eigenvalues of random matrices. A network may be represented by any of several matrices whose set of eigenvalues is the network's spectrum, and can act as a tool in understanding a network's topological and dynamical characteristics. We focus on the spectrum of the graph Laplacian, which is the discretization of the continuous Laplace operator and naturally arises in diffusion and synchronization problems on networks. As a prototypical simple example of spatial networks, we study the ensemble-averaged spectra of random geometric graphs (RGGs) and find that the spectra consist of both a discrete and continuous part. The discrete part, a collection of Dirac delta peaks at integer eigenvalues, does not appear in the spectra of non-spatial graphs and is a direct result of the topology specific to an RGG. We identify two types of mesoscopic symmetric structures that produce integer eigenvalues whose corresponding eigenvectors are exactly localized on the motif and analytically calculate the expected contribution of these motifs to the spectrum of 1d RGGs. Symmetric motifs are of particular interest because the localized eigenvectors imply that mesoscale structures can exist whose dynamics are mostly independent of the embedding network. The continuous part of the spectrum contains groups of eigenvalues that separate from the bulk. We show that the number that separate off together can be deduced by approximating the graph Laplacian with the continuous Laplace operator. Contained within the first separated peak is the smallest nonzero eigenvalue, or algebraic connectivity, whose value is directly related to a network's attack tolerance. We show that the algebraic connectivity varies as a dimensionally dependent power of the average degree. Additionally, we examine the behavior of eigenvalue separation for large N in several scaling regimes and identify a transition, above which separation is lost, but below which separation remains. The elimination of gaps in the spectrum is significant because it implies a smoother path towards synchronization or consensus formation on a network. Also, an approximation for the expected number of separated peaks is given. Advisors/Committee Members: Bassler, Kevin E. (advisor), Josić, Krešimir (committee member), Ordonez, Carlos (committee member), Reiter, George F. (committee member).

Subjects/Keywords: Complex networks; Spatial networks; Random geometric graphs; Motifs; Graph Laplacian; Eigenvalue spectra; Algebraic connectivity; Eigenvalue separation

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APA (6^th Edition):

Nyberg, A. 1. (2014). The Laplacian Spectra of Random Geometric Graphs. (Doctoral Dissertation). University of Houston. Retrieved from http://hdl.handle.net/10657/1646

Chicago Manual of Style (16^th Edition):

Nyberg, Amy 1975-. “The Laplacian Spectra of Random Geometric Graphs.” 2014. Doctoral Dissertation, University of Houston. Accessed March 30, 2020. http://hdl.handle.net/10657/1646.

MLA Handbook (7^th Edition):

Nyberg, Amy 1975-. “The Laplacian Spectra of Random Geometric Graphs.” 2014. Web. 30 Mar 2020.

Vancouver:

Nyberg A1. The Laplacian Spectra of Random Geometric Graphs. [Internet] [Doctoral dissertation]. University of Houston; 2014. [cited 2020 Mar 30]. Available from: http://hdl.handle.net/10657/1646.

Council of Science Editors:

Nyberg A1. The Laplacian Spectra of Random Geometric Graphs. [Doctoral Dissertation]. University of Houston; 2014. Available from: http://hdl.handle.net/10657/1646

University of Manchester

27. 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 March 30, 2020. 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. 30 Mar 2020.

Vancouver:

Zemaityte M. Theory and Algorithms for Linear Eigenvalue Problems. [Internet] [Doctoral dissertation]. University of Manchester; 2020. [cited 2020 Mar 30]. 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

28. 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 · 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 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 March 30, 2020. 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. 30 Mar 2020.

Vancouver:

Zemaityte M. Theory and algorithms for linear eigenvalue problems. [Internet] [Doctoral dissertation]. University of Manchester; 2020. [cited 2020 Mar 30]. 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

University of South Carolina

29. Dutle, Aaron Michael. Spectra of Hypergraphs.

Degree: PhD, Mathematics, 2012, University of South Carolina

URL: https://scholarcommons.sc.edu/etd/1593

► We present a spectral theory of uniform hypergraphs that closely parallels Spectral Graph Theory. A number of developments building upon classical work has led… (more)

Subjects/Keywords: Mathematics; Physical Sciences and Mathematics; Eigenvalue; Hypergraph; Spectrum

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APA (6^th Edition):

Dutle, A. M. (2012). Spectra of Hypergraphs. (Doctoral Dissertation). University of South Carolina. Retrieved from https://scholarcommons.sc.edu/etd/1593

Chicago Manual of Style (16^th Edition):

Dutle, Aaron Michael. “Spectra of Hypergraphs.” 2012. Doctoral Dissertation, University of South Carolina. Accessed March 30, 2020. https://scholarcommons.sc.edu/etd/1593.

MLA Handbook (7^th Edition):

Dutle, Aaron Michael. “Spectra of Hypergraphs.” 2012. Web. 30 Mar 2020.

Vancouver:

Dutle AM. Spectra of Hypergraphs. [Internet] [Doctoral dissertation]. University of South Carolina; 2012. [cited 2020 Mar 30]. Available from: https://scholarcommons.sc.edu/etd/1593.

Council of Science Editors:

Dutle AM. Spectra of Hypergraphs. [Doctoral Dissertation]. University of South Carolina; 2012. Available from: https://scholarcommons.sc.edu/etd/1593

University of Southern California

30. Zhang, Beijia. Geometric bounds for Markov Chain and brief applications in Monte Carlo methods.

Degree: MS, Statistics, 2010, University of Southern California

URL: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/301124/rec/3027

► Since we have the preliminary fact that the irreducible, aperiodic and reversible Markov Chain can asymptotically converge to a unique stationary distribution, and then the… (more)

Subjects/Keywords: second largest eigenvalue; Markov chain; Monte Carlo; simulation

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APA (6^th Edition):

Zhang, B. (2010). Geometric bounds for Markov Chain and brief applications in Monte Carlo methods. (Masters Thesis). University of Southern California. Retrieved from http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/301124/rec/3027

Chicago Manual of Style (16^th Edition):

Zhang, Beijia. “Geometric bounds for Markov Chain and brief applications in Monte Carlo methods.” 2010. Masters Thesis, University of Southern California. Accessed March 30, 2020. http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/301124/rec/3027.

MLA Handbook (7^th Edition):

Zhang, Beijia. “Geometric bounds for Markov Chain and brief applications in Monte Carlo methods.” 2010. Web. 30 Mar 2020.

Vancouver:

Zhang B. Geometric bounds for Markov Chain and brief applications in Monte Carlo methods. [Internet] [Masters thesis]. University of Southern California; 2010. [cited 2020 Mar 30]. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/301124/rec/3027.

Council of Science Editors:

Zhang B. Geometric bounds for Markov Chain and brief applications in Monte Carlo methods. [Masters Thesis]. University of Southern California; 2010. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/301124/rec/3027

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Open Access Theses and Dissertations