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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)
▼ 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 quadratic cost. The LQ design method is important because it yields controllers with a number of desirable properties...
A thesis submitted to the Department of Mathematics, Kwame Nkrumah University of Science and Technology in partial fulfillment for the degree of Doctor of Philosophy in Mathematics, 2013.
KNUST
Subjects/Keywords: Linear-Quadratic; Eigenvalue
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APA (6th 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 (16th Edition):
Kayode, Oladejo Nathaniel. “Linear-quadratic optimal control as an inverse eigenvalue problem.” 2013. Thesis, Kwame Nkrumah University of Science and Technology. Accessed April 10, 2021.
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 (7th Edition):
Kayode, Oladejo Nathaniel. “Linear-quadratic optimal control as an inverse eigenvalue problem.” 2013. Web. 10 Apr 2021.
Vancouver:
Kayode ON. Linear-quadratic optimal control as an inverse eigenvalue problem. [Internet] [Thesis]. Kwame Nkrumah University of Science and Technology; 2013. [cited 2021 Apr 10].
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 λn/λm of the Sturm-Liouville equation with Dirichlet boundary conditions on (0, Ï). In 2005,…
(more)
▼ In this thesis, we study the optimal estimate of
eigenvalue ratios λ
n/λ
m of the
Sturm-Liouville equation with Dirichlet boundary conditions on (0, Ï). In 2005, Horvath and Kiss [10] showed that λ
n/λ
m≤(n/m)
2 when the potential function q ≥ 0 and is a single-well function. Also this is an optimal upper estimate, for equality holds if and only if q = 0. Their result gives a positive answer to a problem posed by Ashbaugh and Benguria [2], who earlier showed that λ
n/λ
1≤n
2 when q ≥ 0.
Here we first simplify the proof of Horvath and Kiss [10]. We use a modified Prufer substitutiony(x)=r(x)sin(Ïθ(x)), y'(x)=r(x)Ïcos(Ïθ(x)), where Ï =
âλ. This modified phase seems to be more effective than the phases Ï and Ï that
Horvath and Kiss [10] used. Furthermore our approach can be generalized to study
the one-dimensional p-Laplacian
eigenvalue problem. We show that for the Dirichlet
problem of the equation -[(y')^(p-1)]'=(p-1)(λ-q)y^(p-1), where p > 1 and f^(p-1)=|f|^(p-1)sgn f =|f|^(p-2)f. The
eigenvalue ratios satisfies λ
n/λ
m≤(n/m)
p, assuming that q(x) ≥ 0 and q is a single-well function on the domain (0, Ï
p). Again this is an optimal upper estimate.
Advisors/Committee Members: Chun-Kong Law (committee member), Tzon-Tzer Lu (chair), Fu-Chuen Chang (chair), Wei-Cheng Lian (chair).
Subjects/Keywords: Eigenvalue ratio; Sturm-Liouville equation
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APA (6th 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 (16th Edition):
Chen, Chao-Zhong. “Optimal upper bounds of eigenvalue ratios for the p-Laplacian.” 2008. Thesis, NSYSU. Accessed April 10, 2021.
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 (7th Edition):
Chen, Chao-Zhong. “Optimal upper bounds of eigenvalue ratios for the p-Laplacian.” 2008. Web. 10 Apr 2021.
Vancouver:
Chen C. Optimal upper bounds of eigenvalue ratios for the p-Laplacian. [Internet] [Thesis]. NSYSU; 2008. [cited 2021 Apr 10].
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
Baylor University
3.
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)
▼ 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 to (2n+1)-order and (3n+2)-order boundary value problems. Methods used for these results involve the theory of u
0-positive operators with respect to a cone in conjunction with sign properties of Green's functions. Finally, initial results are established for the existence of positive solutions for singular two point boundary value problems for a fifth order nonlinear differential equation. The methods involve application of a fixed point theorem for decreasing operators.
Advisors/Committee Members: Henderson, Johnny. (advisor).
Subjects/Keywords: Eigenvalue. Comparison. Boundary Value.
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APA (6th 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 (16th 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 April 10, 2021.
http://hdl.handle.net/2104/9631.
MLA Handbook (7th 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. 10 Apr 2021.
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 2021 Apr 10].
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
University of Iowa
4.
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)
▼ The fundamental process that lies at the foundation of batteries, capacitors, and solar cells is the electron transfer process. This takes place at an interface or boundary in each device and is governed by its corresponding chemical reaction. Making these devices more efficient can help decrease our negative impact on the environment. Recent experiments in the field of Electrochemistry demonstrate that sound waves act as a catalyst for these electron transfer reactions. A model is developed using an Euler equation (conservation of momentum), conservation of mass equation, boundary motion equation, and surface tension equation. Chemically, it is clear that the catalytic phenomenon is derived from the sound waves and how they are affected by the top boundary. When combining these four equations we arrive at a boundary condition involving the top boundary only. We place this condition and the other contributing boundary and initial conditions on the wave equation to understand the interaction that occurs between the waves and the cell. We establish a self-adjoint operator and further use its inverse. Overall, using the Variational form and the Galerkin Method an approximation converges to the solution of the wave equation. With the help of MATLAB these eigenfunctions can be articulated as standing waves.
Advisors/Committee Members: Ströhmer, Gerhard (supervisor).
Subjects/Keywords: Eigenvalue; Electrochemistry; Applied Mathematics
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APA ·
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APA (6th 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 (16th Edition):
Landgren, Jeffrey K. “An acoustic eigenvalue problem and its application to electrochemistry.” 2016. Doctoral Dissertation, University of Iowa. Accessed April 10, 2021.
https://ir.uiowa.edu/etd/2104.
MLA Handbook (7th Edition):
Landgren, Jeffrey K. “An acoustic eigenvalue problem and its application to electrochemistry.” 2016. Web. 10 Apr 2021.
Vancouver:
Landgren JK. An acoustic eigenvalue problem and its application to electrochemistry. [Internet] [Doctoral dissertation]. University of Iowa; 2016. [cited 2021 Apr 10].
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
Georgia State University
5.
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)
▼ In this work we discover for the first time a strong relationship between Geršgorin theory and the geometric multiplicities of eigenvalues. In fact, if λ is an
eigenvalue of an n × n matrix A with geometric multiplicity k, then λ is in at least k Geršgorin discs of A. Moreover, construct the matrix C by replacing, in every row, the (k − 1) smallest off-diagonal entries in absolute value by 0, then λ is in at least k Geršgorin discs of C. We also state and prove many new applications and consequences of these results as well as we update an improve some important existing ones.
Advisors/Committee Members: Frank. J. Hall.
Subjects/Keywords: Geršgorin; eigenvalue; geometric multiplicity
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APA ·
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APA (6th 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 (16th Edition):
Marsli, Rachid. “New Extensions and Applications of Geršgorin Theory.” 2015. Doctoral Dissertation, Georgia State University. Accessed April 10, 2021.
https://scholarworks.gsu.edu/math_diss/26.
MLA Handbook (7th Edition):
Marsli, Rachid. “New Extensions and Applications of Geršgorin Theory.” 2015. Web. 10 Apr 2021.
Vancouver:
Marsli R. New Extensions and Applications of Geršgorin Theory. [Internet] [Doctoral dissertation]. Georgia State University; 2015. [cited 2021 Apr 10].
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
Texas A&M University
6.
McGraw, Carolyn Nicole.
Resolution Requirements for Accurate Reactor Calculations Using the Linear Discontinuous Finite Element Method.
Degree: PhD, Nuclear Engineering, 2020, Texas A&M University
URL: http://hdl.handle.net/1969.1/191771
► This work seeks to ascertain the accuracy of the Linear Discontinuous Finite Element Method (LD) for the spatial variable in realistic neutron-transport calculations for nuclear…
(more)
▼ This work seeks to ascertain the accuracy of the Linear Discontinuous Finite Element Method (LD) for the spatial variable in realistic neutron-transport calculations for nuclear reactors. Our results have shown that LD is an excellent alternative to other methods, such as the Method of Characteristics, for computing these types of problems.
We have implemented the Linear Discontinuous Finite Element Method (LD) in the massively parallel transport code PDT. We ran problems with a range of spatial, angular, and energy discretization choices. We then analyzed the spatial accuracy in these problems. From this analysis, we have determined spatial resolution requirements necessary when calculating accurate solutions using LD. For a typical 2D PWR reactor assembly, using 76 spatial cells per pin cell, we achieve an accuracy of 3 pcm in k-effective. Also we achieve an accuracy of 3 pcm in the pin power we see in the 4 fuel pins we looked at.
We have also developed an error model that accurately predicts quantities of interest at infinite resolution. This model treats both spatial and angular discretization error for a given energy discretization. The model is ‘trained’ using a series of training points - a range of spatial and angular discretization choices and the corresponding QOI. The model then uses a least squares approach to fit the QOIs as a function of our discretization choices. The model quantifies the error in our computations when the mesh is not infinitely refined. This is important for not only predicting solutions to large scale problems that cannot be run but also for quantifying the accuracy of solutions to problems that can.
We have also compared to the Method of Characteristics (MOC) for a range of problems in 2D and 3D. Through our collaboration with researchers from the University of Michigan and their MOC code MPACT, we have determined that for problems with geometric features or boundary layers that are extremely small relative to the problem domain, LD achieves higher accuracy with similar meshes when compared to MOC. This is due to the fact that the Method of Characteristics must use small track spacing to accurately resolve fine mesh attributes. This leads to large numbers of unknowns, compared to DFEMs, to compute solutions to problems with similar levels of accuracy.
Finally we have observed the phenomenon of unphysical oscillations that appear in LD solutions to k-
eigenvalue problems in which both the problem domain and the spatial cells have high aspect ratios. We have explained why and for what types of meshes these oscillations occur. We can now predict, for simple problems, both the scalar flux shape and the k-
eigenvalue for problems with and without unphysical oscillations.
Advisors/Committee Members: Adams, Marvin (advisor), Morel, Jim (committee member), Ragusa, Jean (committee member), Amato, Nancy (committee member).
Subjects/Keywords: LD; k-eigenvalue; nuclear
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Record Details
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❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
McGraw, C. N. (2020). Resolution Requirements for Accurate Reactor Calculations Using the Linear Discontinuous Finite Element Method. (Doctoral Dissertation). Texas A&M University. Retrieved from http://hdl.handle.net/1969.1/191771
Chicago Manual of Style (16th Edition):
McGraw, Carolyn Nicole. “Resolution Requirements for Accurate Reactor Calculations Using the Linear Discontinuous Finite Element Method.” 2020. Doctoral Dissertation, Texas A&M University. Accessed April 10, 2021.
http://hdl.handle.net/1969.1/191771.
MLA Handbook (7th Edition):
McGraw, Carolyn Nicole. “Resolution Requirements for Accurate Reactor Calculations Using the Linear Discontinuous Finite Element Method.” 2020. Web. 10 Apr 2021.
Vancouver:
McGraw CN. Resolution Requirements for Accurate Reactor Calculations Using the Linear Discontinuous Finite Element Method. [Internet] [Doctoral dissertation]. Texas A&M University; 2020. [cited 2021 Apr 10].
Available from: http://hdl.handle.net/1969.1/191771.
Council of Science Editors:
McGraw CN. Resolution Requirements for Accurate Reactor Calculations Using the Linear Discontinuous Finite Element Method. [Doctoral Dissertation]. Texas A&M University; 2020. Available from: http://hdl.handle.net/1969.1/191771
Texas A&M University
7.
McGraw, Carolyn Nicole.
Resolution Requirements for Accurate Reactor Calculations Using the Linear Discontinuous Finite Element Method.
Degree: PhD, Nuclear Engineering, 2020, Texas A&M University
URL: http://hdl.handle.net/1969.1/191764
► This work seeks to ascertain the accuracy of the Linear Discontinuous Finite Element Method (LD) for the spatial variable in realistic neutron-transport calculations for nuclear…
(more)
▼ This work seeks to ascertain the accuracy of the Linear Discontinuous Finite Element Method (LD) for the spatial variable in realistic neutron-transport calculations for nuclear reactors. Our results have shown that LD is an excellent alternative to other methods, such as the Method of Characteristics, for computing these types of problems.
We have implemented the Linear Discontinuous Finite Element Method (LD) in the massively parallel transport code PDT. We ran problems with a range of spatial, angular, and energy discretization choices. We then analyzed the spatial accuracy in these problems. From this analysis, we have determined spatial resolution requirements necessary when calculating accurate solutions using LD. For a typical 2D PWR reactor assembly, using 76 spatial cells per pin cell, we achieve an accuracy of 3 pcm in k-effective. Also we achieve an accuracy of 3 pcm in the pin power we see in the 4 fuel pins we looked at.
We have also developed an error model that accurately predicts quantities of interest at infinite resolution. This model treats both spatial and angular discretization error for a given energy discretization. The model is ‘trained’ using a series of training points - a range of spatial and angular discretization choices and the corresponding QOI. The model then uses a least squares approach to fit the QOIs as a function of our discretization choices. The model quantifies the error in our computations when the mesh is not infinitely refined. This is important for not only predicting solutions to large scale problems that cannot be run but also for quantifying the accuracy of solutions to problems that can.
We have also compared to the Method of Characteristics (MOC) for a range of problems in 2D and 3D. Through our collaboration with researchers from the University of Michigan and their MOC code MPACT, we have determined that for problems with geometric features or boundary layers that are extremely small relative to the problem domain, LD achieves higher accuracy with similar meshes when compared to MOC. This is due to the fact that the Method of Characteristics must use small track spacing to accurately resolve fine mesh attributes. This leads to large numbers of unknowns, compared to DFEMs, to compute solutions to problems with similar levels of accuracy.
Finally we have observed the phenomenon of unphysical oscillations that appear in LD solutions to k-
eigenvalue problems in which both the problem domain and the spatial cells have high aspect ratios. We have explained why and for what types of meshes these oscillations occur. We can now predict, for simple problems, both the scalar flux shape and the k-
eigenvalue for problems with and without unphysical oscillations.
Advisors/Committee Members: Adams, Marvin (advisor), Morel, Jim (committee member), Ragusa, Jean (committee member), Amato, Nancy (committee member).
Subjects/Keywords: LD; k-eigenvalue; nuclear
Record Details
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Record Details
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❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
McGraw, C. N. (2020). Resolution Requirements for Accurate Reactor Calculations Using the Linear Discontinuous Finite Element Method. (Doctoral Dissertation). Texas A&M University. Retrieved from http://hdl.handle.net/1969.1/191764
Chicago Manual of Style (16th Edition):
McGraw, Carolyn Nicole. “Resolution Requirements for Accurate Reactor Calculations Using the Linear Discontinuous Finite Element Method.” 2020. Doctoral Dissertation, Texas A&M University. Accessed April 10, 2021.
http://hdl.handle.net/1969.1/191764.
MLA Handbook (7th Edition):
McGraw, Carolyn Nicole. “Resolution Requirements for Accurate Reactor Calculations Using the Linear Discontinuous Finite Element Method.” 2020. Web. 10 Apr 2021.
Vancouver:
McGraw CN. Resolution Requirements for Accurate Reactor Calculations Using the Linear Discontinuous Finite Element Method. [Internet] [Doctoral dissertation]. Texas A&M University; 2020. [cited 2021 Apr 10].
Available from: http://hdl.handle.net/1969.1/191764.
Council of Science Editors:
McGraw CN. Resolution Requirements for Accurate Reactor Calculations Using the Linear Discontinuous Finite Element Method. [Doctoral Dissertation]. Texas A&M University; 2020. Available from: http://hdl.handle.net/1969.1/191764
Texas A&M University
8.
McGraw, Carolyn Nicole.
Resolution Requirements for Accurate Reactor Calculations Using the Linear Discontinuous Finite Element Method.
Degree: PhD, Nuclear Engineering, 2020, Texas A&M University
URL: http://hdl.handle.net/1969.1/191763
► This work seeks to ascertain the accuracy of the Linear Discontinuous Finite Element Method (LD) for the spatial variable in realistic neutron-transport calculations for nuclear…
(more)
▼ This work seeks to ascertain the accuracy of the Linear Discontinuous Finite Element Method (LD) for the spatial variable in realistic neutron-transport calculations for nuclear reactors. Our results have shown that LD is an excellent alternative to other methods, such as the Method of Characteristics, for computing these types of problems.
We have implemented the Linear Discontinuous Finite Element Method (LD) in the massively parallel transport code PDT. We ran problems with a range of spatial, angular, and energy discretization choices. We then analyzed the spatial accuracy in these problems. From this analysis, we have determined spatial resolution requirements necessary when calculating accurate solutions using LD. For a typical 2D PWR reactor assembly, using 76 spatial cells per pin cell, we achieve an accuracy of 3 pcm in k-effective. Also we achieve an accuracy of 3 pcm in the pin power we see in the 4 fuel pins we looked at.
We have also developed an error model that accurately predicts quantities of interest at infinite resolution. This model treats both spatial and angular discretization error for a given energy discretization. The model is ‘trained’ using a series of training points - a range of spatial and angular discretization choices and the corresponding QOI. The model then uses a least squares approach to fit the QOIs as a function of our discretization choices. The model quantifies the error in our computations when the mesh is not infinitely refined. This is important for not only predicting solutions to large scale problems that cannot be run but also for quantifying the accuracy of solutions to problems that can.
We have also compared to the Method of Characteristics (MOC) for a range of problems in 2D and 3D. Through our collaboration with researchers from the University of Michigan and their MOC code MPACT, we have determined that for problems with geometric features or boundary layers that are extremely small relative to the problem domain, LD achieves higher accuracy with similar meshes when compared to MOC. This is due to the fact that the Method of Characteristics must use small track spacing to accurately resolve fine mesh attributes. This leads to large numbers of unknowns, compared to DFEMs, to compute solutions to problems with similar levels of accuracy.
Finally we have observed the phenomenon of unphysical oscillations that appear in LD solutions to k-
eigenvalue problems in which both the problem domain and the spatial cells have high aspect ratios. We have explained why and for what types of meshes these oscillations occur. We can now predict, for simple problems, both the scalar flux shape and the k-
eigenvalue for problems with and without unphysical oscillations.
Advisors/Committee Members: Adams, Marvin (advisor), Morel, Jim (committee member), Ragusa, Jean (committee member), Amato, Nancy (committee member).
Subjects/Keywords: LD; k-eigenvalue; nuclear
Record Details
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Record Details
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❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
McGraw, C. N. (2020). Resolution Requirements for Accurate Reactor Calculations Using the Linear Discontinuous Finite Element Method. (Doctoral Dissertation). Texas A&M University. Retrieved from http://hdl.handle.net/1969.1/191763
Chicago Manual of Style (16th Edition):
McGraw, Carolyn Nicole. “Resolution Requirements for Accurate Reactor Calculations Using the Linear Discontinuous Finite Element Method.” 2020. Doctoral Dissertation, Texas A&M University. Accessed April 10, 2021.
http://hdl.handle.net/1969.1/191763.
MLA Handbook (7th Edition):
McGraw, Carolyn Nicole. “Resolution Requirements for Accurate Reactor Calculations Using the Linear Discontinuous Finite Element Method.” 2020. Web. 10 Apr 2021.
Vancouver:
McGraw CN. Resolution Requirements for Accurate Reactor Calculations Using the Linear Discontinuous Finite Element Method. [Internet] [Doctoral dissertation]. Texas A&M University; 2020. [cited 2021 Apr 10].
Available from: http://hdl.handle.net/1969.1/191763.
Council of Science Editors:
McGraw CN. Resolution Requirements for Accurate Reactor Calculations Using the Linear Discontinuous Finite Element Method. [Doctoral Dissertation]. Texas A&M University; 2020. Available from: http://hdl.handle.net/1969.1/191763
Iowa State University
9.
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 (6th 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 (16th Edition):
Luo, Cheng. “A comprehensive invariant subspace-based framework for power system small-signal stability analysis.” 2011. Thesis, Iowa State University. Accessed April 10, 2021.
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 (7th Edition):
Luo, Cheng. “A comprehensive invariant subspace-based framework for power system small-signal stability analysis.” 2011. Web. 10 Apr 2021.
Vancouver:
Luo C. A comprehensive invariant subspace-based framework for power system small-signal stability analysis. [Internet] [Thesis]. Iowa State University; 2011. [cited 2021 Apr 10].
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
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)
▼ 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 target system, many of curves will diverge when the homotopy parameter goes to the end. In this case we will have a difficulty in tracing the solution curves by continuation method because tracing divergent curves does not help us obtain any solution of target system but also its computation is very costly. As the parameter goes to the end, how to determine whether a curve converges or diverges effectively for reducing the computational cost is called the end game problem.
In this thesis we will deal with the end game problem via the curve expression theory proposed by Morgan et al. The theory says the homotopy curve for solving polynomial systems can be expressed by Puiseux series expansion when the parameter is nearby the end. Moreover, the exponents of the leading term in Puiseux series determine the convergency of a curve. We also study the algebraic
eigenvalue problems solving by homotopy continuation method. Several observations in numerical experiments for nonderogatory algebraic
eigenvalue problem and its end game problem will be reported.
Advisors/Committee Members: Tzon-Tzer Lu (chair), Tsung-Lin Lee (committee member), Chieh-Sen Huang (chair), Hung-Tsai Huang (chair), Yueh-Cheng Kuo (chair).
Subjects/Keywords: end game problem; eigenvalue problems; homotopy continuation
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APA (6th 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 (16th Edition):
Chang, Hen-wen. “The End Game Problem in Solving Algebraic Eigenvalue Problems by Homotopy Continuation Method.” 2013. Thesis, NSYSU. Accessed April 10, 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 (7th Edition):
Chang, Hen-wen. “The End Game Problem in Solving Algebraic Eigenvalue Problems by Homotopy Continuation Method.” 2013. Web. 10 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 10].
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)
▼ We study the evolutionary of species under the replicator equation with antisymmetric payoff . All of out results show odd number of species survived and its probability distritbution agrees with the combination NCk which is reported by âLarge-Dimensional Replicator Equations with Antisymmetric Random Interactionsâ . Further , the population of survival species is identical with the eigenvector for
eigenvalue zero of a reduced payoff for the survived species .Our results for the partly interaction cases show strong resemblance to the global one till the portion of interaction is roughly less than 10%. That means all species are sort of correlated even though most of them are not directly interacting. Some of results show even number of species survived on specific value since there are isolated points ,we conjecture the measure of even number of survived species in parameter space,i.e, we change continuously a parameter in the payoff table . The relaxation time near the even species is a power law with critical exponent ~1 ,|(γ- γ c)/γc|-1.
Advisors/Committee Members: De-Hone Lin (chair), Wang-Chuang Kuo (committee member), Jing-Yuan Ko (chair).
Subjects/Keywords: Replicator Equation; Game Theory; eigenvalue; Payoff
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APA ·
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APA (6th 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 (16th Edition):
Fu, Wen-Chuan. “The Evolution of Mass Species under the Replicator Equation.” 2014. Thesis, NSYSU. Accessed April 10, 2021.
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 (7th Edition):
Fu, Wen-Chuan. “The Evolution of Mass Species under the Replicator Equation.” 2014. Web. 10 Apr 2021.
Vancouver:
Fu W. The Evolution of Mass Species under the Replicator Equation. [Internet] [Thesis]. NSYSU; 2014. [cited 2021 Apr 10].
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)
▼ 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 Keller [7],Chern-Shen [3], Lavine [8], Huang [4] and Horvath [6] show that the first
eigenvalue gap of the Schrodinger operator under Dirichlet boundary condition and the first
eigenvalue ratioï¼Î»2/λ1ï¼of the string equation under Dirichlet boundary condition are dual problems of each other. Furthermore the problems when the potential functions and density functions are restricted to certain classes of functions can all be solved by a variational calculus method (differentiating the whole equation with respect to a parameter t to find λn'(t)) together with some elementary analysis. In this thesis, we shall give a short survey of these result. In particular, we shall prove 3 pairs of theorems. First when q is convex (Ï is concave), then λ2-λ1â§3 ï¼Î»2/λ1â§4ï¼.If q is a single
well and its transition point is Ï/2 (Ï is a
single barrier and its transition point is Ï/2), then
λ2-λ1â§3ï¼Î»2/λ1â§4ï¼.All these lower bounds are optimal when q(Ï) is constant. Finally when q is bounded (Ï is bounded), then λ2-λ1 is minimized by a step function (λ2/λ1
is minimized by a step function), after some additional
conditions. We shell give a unified treatment to the above
results.
Advisors/Committee Members: W. C. Lian (chair), Chun-Kong Law (committee member), Tzon-Tzer Lu (chair).
Subjects/Keywords: optimal estimates; eigenvalue
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APA ·
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APA (6th 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 (16th Edition):
Huang, Hsien-kuei. “Optimal estimates of the eigenvalue gap and eigenvalue ratio with variational.” 2004. Thesis, NSYSU. Accessed April 10, 2021.
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 (7th Edition):
Huang, Hsien-kuei. “Optimal estimates of the eigenvalue gap and eigenvalue ratio with variational.” 2004. Web. 10 Apr 2021.
Vancouver:
Huang H. Optimal estimates of the eigenvalue gap and eigenvalue ratio with variational. [Internet] [Thesis]. NSYSU; 2004. [cited 2021 Apr 10].
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 λ1' in E[h,H,M],…
(more)
▼ In this thesis, we prove 2 theorems. First let Ï0 be
a minimizing (or maximizing) density function for the first
antiperiodic
eigenvalue λ1' in E[h,H,M], then Ï0=hÏ(a,b)+HÏ[0,Ï]/(a,b) (or Ï0=HÏ(a,b)+hÏ[0,Ï]/(a,b)) a.e. Finally, we prove minλ1'=minμ1=minν1 where μ1 and ν1 are the first Dirichlet and second Neumann eigenvalues, respectively. Furthermore, we determine the jump point X0 of Ï0 and the corresponding
eigenvalue λ1', assuming that Ï0 is symmetric about Ï/2 We derive the nonlinear equations for this jump point X0 and λ1',then use Mathematica to solve the equations numerically.
Advisors/Committee Members: W.C.Lian (chair), Chiu-Ya Lan (chair), Tzon-Tzer Lu (chair), Chun-Kong Law (committee member).
Subjects/Keywords: Density functions; eigenvalue
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APA (6th 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 (16th Edition):
Kung, Shing-Yuan. “Density functions with extremal antiperiodic eigenvalues and related topics.” 2005. Thesis, NSYSU. Accessed April 10, 2021.
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 (7th Edition):
Kung, Shing-Yuan. “Density functions with extremal antiperiodic eigenvalues and related topics.” 2005. Web. 10 Apr 2021.
Vancouver:
Kung S. Density functions with extremal antiperiodic eigenvalues and related topics. [Internet] [Thesis]. NSYSU; 2005. [cited 2021 Apr 10].
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)
▼ 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 simulation using the numerical electromagnetic algorithm, and result in simulated divergence or error. The two reasons of numerical error are passivity and causality, which priginate from the defect in the numerical calculation. In this thesis, for this problem, investigate the numerical compensation method for passivity, The occurrence of passive will make the frequency point of power is negative, this will makes the system divergence, Improve this problem, passivity verification and enforcement by
eigenvalue in the Y-parameter, in the S-parameter by the singular value, causality conditions must be match with the imaginary part and the real part relationship, such as the Hilbert transform or the Kramer-Kronig relation, can be used to make causal verification and enforcement.
Through some numerical methods, used simulation software such as: HFSS, ADS simulation of the microwave circuit model extraction, modified singular value,
eigenvalue, and reached to reduce the numerical error, let it satisfy the convergence and avoid incorrect results, and minimize the impact of the initial data, does not change the characteristics of the original module, but also to solve the passive and the issue of causality.
Advisors/Committee Members: Ken-Huang Lin (chair), Chih-Wen Kuo (committee member), Chie-In Lee (chair), Ming-Cheng Liang (chair).
Subjects/Keywords: Singular Value; Eigenvalue; Causality; Passivity; Hilbert Transform
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APA (6th 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 (16th Edition):
Chan, Yu-Lin. “A Numerical Method to Solve the Divergence Issue of Microwave Circuit Model Extraction.” 2012. Thesis, NSYSU. Accessed April 10, 2021.
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 (7th Edition):
Chan, Yu-Lin. “A Numerical Method to Solve the Divergence Issue of Microwave Circuit Model Extraction.” 2012. Web. 10 Apr 2021.
Vancouver:
Chan Y. A Numerical Method to Solve the Divergence Issue of Microwave Circuit Model Extraction. [Internet] [Thesis]. NSYSU; 2012. [cited 2021 Apr 10].
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 (6th 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 (16th Edition):
Rommes, J. “Methods for eigenvalue problems with applications in model order reduction.” 2007. Doctoral Dissertation, Universiteit Utrecht. Accessed April 10, 2021.
http://dspace.library.uu.nl:8080/handle/1874/21787.
MLA Handbook (7th Edition):
Rommes, J. “Methods for eigenvalue problems with applications in model order reduction.” 2007. Web. 10 Apr 2021.
Vancouver:
Rommes J. Methods for eigenvalue problems with applications in model order reduction. [Internet] [Doctoral dissertation]. Universiteit Utrecht; 2007. [cited 2021 Apr 10].
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
North Carolina State University
16.
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 (6th 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 (16th Edition):
Liu, Ning. “Spectral Clustering for Graphs and Markov Chains.” 2010. Doctoral Dissertation, North Carolina State University. Accessed April 10, 2021.
http://www.lib.ncsu.edu/resolver/1840.16/4886.
MLA Handbook (7th Edition):
Liu, Ning. “Spectral Clustering for Graphs and Markov Chains.” 2010. Web. 10 Apr 2021.
Vancouver:
Liu N. Spectral Clustering for Graphs and Markov Chains. [Internet] [Doctoral dissertation]. North Carolina State University; 2010. [cited 2021 Apr 10].
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
Baylor University
17.
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)
▼ 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 = 0 and u⁽⁴⁾ + λ₂q(x)u = 0, 0 ≤ x ≤ 1, with each satisfying the boundary conditions u(0) = u′(r) = u″(r) = u‴(1) = 0, 0 < r < 1. The existence of smallest positive eigenvalues is established, and a comparison theorem for smallest positive eigenvalues is obtained. These results are then extended to the nth order problem using two different methods. One method involves finding the Green's function for –u⁽ⁿ⁾ = 0 satisfying the higher order boundary conditions, and the other involves making a substitution that allows us to work with a variation of the fourth order problem. Extremal points via Krein-Rutman theory are then found. Analogous results are then obtained for the
eigenvalue problems u‴ + λ₁p(x)u = 0 and u‴ + λ₂q(x)u = 0, with each satisfying u(0) = u′(r) = u″(1) = 0, 0 < 1/2 < r < 1.
Advisors/Committee Members: Henderson, Johnny. (advisor).
Subjects/Keywords: Differential equations.; Eigenvalue problems.; Extremal points.
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APA (6th 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 (16th 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 April 10, 2021.
http://hdl.handle.net/2104/8235.
MLA Handbook (7th Edition):
Neugebauer, Jeffrey T. “Comparison of smallest eigenvalues and extremal points for third and fourth order three point boundary value problems.” 2011. Web. 10 Apr 2021.
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 2021 Apr 10].
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
Universitat Politècnica de València
18.
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 (6th 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 (16th Edition):
Romero Alcalde, Eloy. “Parallel implementation of Davidson-type methods for large-scale eigenvalue problems
.” 2012. Doctoral Dissertation, Universitat Politècnica de València. Accessed April 10, 2021.
http://hdl.handle.net/10251/15188.
MLA Handbook (7th Edition):
Romero Alcalde, Eloy. “Parallel implementation of Davidson-type methods for large-scale eigenvalue problems
.” 2012. Web. 10 Apr 2021.
Vancouver:
Romero Alcalde E. Parallel implementation of Davidson-type methods for large-scale eigenvalue problems
. [Internet] [Doctoral dissertation]. Universitat Politècnica de València; 2012. [cited 2021 Apr 10].
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
University of Minnesota
19.
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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Manager
APA (6th 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 (16th 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 April 10, 2021.
http://hdl.handle.net/11299/165538.
MLA Handbook (7th Edition):
Kakade, Virendra Vilas. “Eigenvalue based alternans prediction and the effects of heart rate variability on alternans formation.” 2013. Web. 10 Apr 2021.
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 2021 Apr 10].
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
20.
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)
▼ 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 acceleration degrade. This occurs in higher dimensional heterogeneous problems [51]. We focus on utilizing homotopy continuation as a means of providing a better initial guess for difficult problems. We investigate various homotopy formulations for two primary diffcult problems: a thick-diffusive fixed internal source, and a k-
eigenvalue problem with high dominance ratio. We also investigate the usefulness of homotopy continuation for computationally intensive problems with 30-energy groups. We find that homotopy continuation exhibits usefulness in specific problem formulations. In the thick-diffusive problem it shows benefit when there is a strong internal source in thin materials. In the k-
eigenvalue problem, homotopy continuation provides an improvement in convergence speed for fixed point iteration methods in high dominance ratio problems. We also show that one of our imbeddings successfully stabilizes the nonlinear formulation of the k-
eigenvalue problem with a high dominance ratio.
Advisors/Committee Members: Prinja, Anil, Warsa, Jim, Coutsias, Evangelos, De Oliveira, Cassiano.
Subjects/Keywords: Homotopy; Sn; Continuation; Transport; Eigenvalue; Diffusive
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APA (6th 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 (16th Edition):
Myers, Nicholas. “An Sn Application of Homotopy Continuation in Neutral Particle Transport.” 2014. Doctoral Dissertation, University of New Mexico. Accessed April 10, 2021.
http://hdl.handle.net/1928/24581.
MLA Handbook (7th Edition):
Myers, Nicholas. “An Sn Application of Homotopy Continuation in Neutral Particle Transport.” 2014. Web. 10 Apr 2021.
Vancouver:
Myers N. An Sn Application of Homotopy Continuation in Neutral Particle Transport. [Internet] [Doctoral dissertation]. University of New Mexico; 2014. [cited 2021 Apr 10].
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
21.
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)
▼ 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, including jack-knifing, trailer sway, and roll-over. To address this CT stability problem, two ATDB controllers are proposed, which are designed using the Linear Quadratic Regulator (LQR) and ??????? robust control techniques. In order to design the ATDB controllers, a linear 3 degrees of freedom (DOF) and a linear 5-DOF model are generated and validated with a nonlinear CT model derived using CarSim software.
Eigenvalue analysis is conducted to examine the effects of typical trailer parameters on the lateral stability of CT combinations. The contribution of the LQR-based ATDB controller to the enhancement of CT stability is assessed. The thesis also investigates the insensitivity of the ??????? controller to parameter uncertainties. A genetic algorithm (GA) is applied to find optimal control variables of the active safety systems. Numerical simulations demonstrate that the parametric study may provide a guideline for trailer design variable selections, and the proposed ATDB systems can effectively increase the safety of CT combinations.
Advisors/Committee Members: He, Yuping.
Subjects/Keywords: ATDB; Genetic algorithm; LQR; Mu synthesis; Eigenvalue
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APA (6th 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 (16th Edition):
Lee, Eungkil. “Design optimization of active trailer differential braking systems for car-trailer combinations.” 2016. Thesis, University of Ontario Institute of Technology. Accessed April 10, 2021.
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 (7th Edition):
Lee, Eungkil. “Design optimization of active trailer differential braking systems for car-trailer combinations.” 2016. Web. 10 Apr 2021.
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 2021 Apr 10].
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
University of Arizona
22.
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)
▼ 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 able to apply Householder reflections to separate the random variables corresponding to the spectrum from all other variables in the random Gaussian Matrix. In this thesis, motivated by ideas coming from generalized subgroup algorithms as well as Edelman’s techniques, we make significant inroads on extending this type of spectral analysis to the much more challenging case of the Hamiltonian matrix ensemble.
Advisors/Committee Members: Ercolani, Nicholas (advisor), Kennedy, Tom (committeemember), Watkins, Joe (committeemember), Glickenstein, David (committeemember).
Subjects/Keywords: Density;
Eigenvalue;
Ginibre;
Hamiltonian;
Probability;
Spectrum
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APA (6th 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 (16th Edition):
Fox, Matthew Kins. “Spectrum of Hamiltonian Matrices
.” 2018. Doctoral Dissertation, University of Arizona. Accessed April 10, 2021.
http://hdl.handle.net/10150/628423.
MLA Handbook (7th Edition):
Fox, Matthew Kins. “Spectrum of Hamiltonian Matrices
.” 2018. Web. 10 Apr 2021.
Vancouver:
Fox MK. Spectrum of Hamiltonian Matrices
. [Internet] [Doctoral dissertation]. University of Arizona; 2018. [cited 2021 Apr 10].
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 Arkansas
23.
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)
▼ The eigenvalues and eigenvectors of a Hessenberg matrix, H, are computed with a combination of homotopy increments and the Arnoldi method. Given a set, Ω, of approximate eigenvalues of H, there exists a unique vector f = f(H,Ω) in Rn where λ(H-e<sub>1ft)=Ω. A diagonalization of the homotopy H(t)=H−(1−t)e
1ft at t=0 provides a prediction of the eigenvalues of H(t) at later times. These predictions define a new Ω that defines a new homotopy. The correction for each eigenvalue has an O(t2) error estimate, enabling variable step size and efficient convergence tests. Computations are done primarily in real arithmetic, and bifurcations are avoided by restarting the homotopy with Arnoldi eigenvalues. Although the method is neither as elegant nor as robust as the QR algorithm, it is about twice as fast in the randomly generated examples considered and is highly parallelizable.</sub>
Advisors/Committee Members: Mark Arnold, Yo'av Rieck, William Feldman.
Subjects/Keywords: Arnoldi; Continuation; Eigenvalue; Homotopy; Applied Mathematics
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APA (6th 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 (16th Edition):
Hutchison, Brandon. “A Restarted Homotopy Method for the Nonsymmetric Eigenvalue Problem.” 2011. Doctoral Dissertation, University of Arkansas. Accessed April 10, 2021.
https://scholarworks.uark.edu/etd/74.
MLA Handbook (7th Edition):
Hutchison, Brandon. “A Restarted Homotopy Method for the Nonsymmetric Eigenvalue Problem.” 2011. Web. 10 Apr 2021.
Vancouver:
Hutchison B. A Restarted Homotopy Method for the Nonsymmetric Eigenvalue Problem. [Internet] [Doctoral dissertation]. University of Arkansas; 2011. [cited 2021 Apr 10].
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 Waterloo
24.
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)
▼ 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 eigenvalue and projected eigenvalue techniques, convex quadratic programming techniques, and semidefinite programming (SDP). In particular, we show that the SDP relaxation is equivalent to and arises from the Lagrangian relaxation for a particular quadratically constrained quadratic model. Moreover, the bounds obtained by the eigenvalue techniques are good and cheap.
Subjects/Keywords: Graph Partitioning; Semidefinite Programming; eigenvalue bounds
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to Zotero / EndNote / Reference
Manager
APA (6th 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 (16th Edition):
Wang, Ningchuan. “Eigenvalue, Quadratic Programming and Semidefinite Programming Bounds for Graph Partitioning Problems.” 2014. Thesis, University of Waterloo. Accessed April 10, 2021.
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 (7th Edition):
Wang, Ningchuan. “Eigenvalue, Quadratic Programming and Semidefinite Programming Bounds for Graph Partitioning Problems.” 2014. Web. 10 Apr 2021.
Vancouver:
Wang N. Eigenvalue, Quadratic Programming and Semidefinite Programming Bounds for Graph Partitioning Problems. [Internet] [Thesis]. University of Waterloo; 2014. [cited 2021 Apr 10].
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
University of Georgia
25.
Lavoie, Michael Rob.
A parallel approach to DICCCOL.
Degree: 2015, University of Georgia
URL: http://hdl.handle.net/10724/30976
► DICCCOL is a process that identifies common connectivity in the brain. It was developed to show that the cortex has a common structure thereby identifying…
(more)
▼ DICCCOL is a process that identifies common connectivity in the brain. It was developed to show that the cortex has a common structure thereby identifying functional correspondence. The tool compares the connectivity in a subject brain
against a reference library of structural correspondence. A set of bundles is processed for comparison against this library. The result is a subject’s fiber bundle that most closely matches the libraries reference bundle. The data set is relatively small
but the processing is extensive. A single thread approach to the process is very time consuming. This task is better suited for a parallel processing approach. I show how the work can be accomplished more efficiently with GPU hardware and CUDA’s parallel
programming, resulting in a speedup factor of better than 6.
Subjects/Keywords: DICCCOL; CUDA; GPGPU; eigenvector; eigenvalue; medical imaging
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APA (6th Edition):
Lavoie, M. R. (2015). A parallel approach to DICCCOL. (Thesis). University of Georgia. Retrieved from http://hdl.handle.net/10724/30976
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Lavoie, Michael Rob. “A parallel approach to DICCCOL.” 2015. Thesis, University of Georgia. Accessed April 10, 2021.
http://hdl.handle.net/10724/30976.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Lavoie, Michael Rob. “A parallel approach to DICCCOL.” 2015. Web. 10 Apr 2021.
Vancouver:
Lavoie MR. A parallel approach to DICCCOL. [Internet] [Thesis]. University of Georgia; 2015. [cited 2021 Apr 10].
Available from: http://hdl.handle.net/10724/30976.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Lavoie MR. A parallel approach to DICCCOL. [Thesis]. University of Georgia; 2015. Available from: http://hdl.handle.net/10724/30976
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
University of Canterbury
26.
Pons, Arion Douglas.
Aeroelastic flutter as a multiparameter eigenvalue problem.
Degree: M. Eng., Mechanical Engineering, 2015, University of Canterbury
URL: http://dx.doi.org/10.26021/1438
► In this thesis we explore the relationship between aeroelastic flutter and multiparameter spectral theory. We first introduce the basic concept of the relationship between these…
(more)
▼ In this thesis we explore the relationship between aeroelastic flutter and multiparameter spectral theory. We first introduce the basic concept of the relationship between these two fields in abstract terms. Then we expand on this initial concept, using it to devise visualisation methods and a wide variety of solvers for flutter problems. We assess these solvers, applying them to real-life aeroelastic systems and measuring their performance. We then discuss and devise methods for improving these solvers. All our conclusions are supported by a variety of evidence from numerical experiments. Finally, we assess all of our methods, providing recommendations as to their use and future development.
We do achieve several things in this thesis which have not been achieved before. Firstly, we solved a non-trivial flutter problem with a direct solver. The only direct solvers that have previously been presented are those that arise from classical flutter analysis, which applies only to very simple systems. Secondly, and as an extension of this first point, we solved a system with Theodorsen aerodynamics (approximated by a highly accurately) with a direct solver. This was achieved in an industrially competitive time (0.2s). This has never before been achieved. Thirdly, we solved an unstructured multiparameter eigenvalue problem. Unstructured problems have not been considered before, even in theoretical literature. This result is thus of significance both for multiparameter spectral theory and aeroelasticity. However, the single most important contribution of this thesis is the opening of a whole new field of study which stretches beyond aeroelasticity and into other industries: the treatment of instability problems using multiparameter methods. This field of research is wide and untrodden, and has the potential to change the way we analyse instability across many industries.
Subjects/Keywords: aeroelasticity; flutter; multiparameter; eigenvalue; instability; aerodynamics; vibration
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APA (6th Edition):
Pons, A. D. (2015). Aeroelastic flutter as a multiparameter eigenvalue problem. (Masters Thesis). University of Canterbury. Retrieved from http://dx.doi.org/10.26021/1438
Chicago Manual of Style (16th Edition):
Pons, Arion Douglas. “Aeroelastic flutter as a multiparameter eigenvalue problem.” 2015. Masters Thesis, University of Canterbury. Accessed April 10, 2021.
http://dx.doi.org/10.26021/1438.
MLA Handbook (7th Edition):
Pons, Arion Douglas. “Aeroelastic flutter as a multiparameter eigenvalue problem.” 2015. Web. 10 Apr 2021.
Vancouver:
Pons AD. Aeroelastic flutter as a multiparameter eigenvalue problem. [Internet] [Masters thesis]. University of Canterbury; 2015. [cited 2021 Apr 10].
Available from: http://dx.doi.org/10.26021/1438.
Council of Science Editors:
Pons AD. Aeroelastic flutter as a multiparameter eigenvalue problem. [Masters Thesis]. University of Canterbury; 2015. Available from: http://dx.doi.org/10.26021/1438
Wayne State University
27.
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 (6th 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 (16th Edition):
Hu, Jiaxi. “Shape Analysis Using Spectral Geometry.” 2015. Doctoral Dissertation, Wayne State University. Accessed April 10, 2021.
https://digitalcommons.wayne.edu/oa_dissertations/1143.
MLA Handbook (7th Edition):
Hu, Jiaxi. “Shape Analysis Using Spectral Geometry.” 2015. Web. 10 Apr 2021.
Vancouver:
Hu J. Shape Analysis Using Spectral Geometry. [Internet] [Doctoral dissertation]. Wayne State University; 2015. [cited 2021 Apr 10].
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
28.
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)
▼ 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 Q(λ)=λ
2M+λD+S that
satisfy Q(λ)=0, can be obtained iteratively and without linearizing
the problem. However, many iterative methods can only find some of
the solutions λ. Therefore, we are going to modify a method based
on Newton iterations in order to find all of the solutions λ, that
are known also as the eigenvalues of the QEP. In addition, we will
investigate how the proposed method compares with standard
iterative methods from the literature. Moreover, we will provide a
method for finding an upper bound for the number of the eigenvalues
of the QEP, and apply this in our method for the purpose of finding
all solutions λ.
Advisors/Committee Members: Pollock, Sara (Advisor).
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 (6th 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 (16th Edition):
Ali, Ali Hasan. “Modifying Some Iterative Methods for Solving Quadratic
Eigenvalue Problems.” 2017. Masters Thesis, Wright State University. Accessed April 10, 2021.
http://rave.ohiolink.edu/etdc/view?acc_num=wright1515029541712239.
MLA Handbook (7th Edition):
Ali, Ali Hasan. “Modifying Some Iterative Methods for Solving Quadratic
Eigenvalue Problems.” 2017. Web. 10 Apr 2021.
Vancouver:
Ali AH. Modifying Some Iterative Methods for Solving Quadratic
Eigenvalue Problems. [Internet] [Masters thesis]. Wright State University; 2017. [cited 2021 Apr 10].
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 Manchester
29.
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 ·
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MLA ·
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CSE |
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Manager
APA (6th 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 (16th Edition):
Zemaityte, Mante. “Theory and Algorithms for Linear Eigenvalue
Problems.” 2020. Doctoral Dissertation, University of Manchester. Accessed April 10, 2021.
http://www.manchester.ac.uk/escholar/uk-ac-man-scw:323865.
MLA Handbook (7th Edition):
Zemaityte, Mante. “Theory and Algorithms for Linear Eigenvalue
Problems.” 2020. Web. 10 Apr 2021.
Vancouver:
Zemaityte M. Theory and Algorithms for Linear Eigenvalue
Problems. [Internet] [Doctoral dissertation]. University of Manchester; 2020. [cited 2021 Apr 10].
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 Houston
30.
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 (6th 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 (16th Edition):
Nyberg, Amy 1975-. “The Laplacian Spectra of Random Geometric Graphs.” 2014. Doctoral Dissertation, University of Houston. Accessed April 10, 2021.
http://hdl.handle.net/10657/1646.
MLA Handbook (7th Edition):
Nyberg, Amy 1975-. “The Laplacian Spectra of Random Geometric Graphs.” 2014. Web. 10 Apr 2021.
Vancouver:
Nyberg A1. The Laplacian Spectra of Random Geometric Graphs. [Internet] [Doctoral dissertation]. University of Houston; 2014. [cited 2021 Apr 10].
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
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