Multiparameter Eingenvalue Problems
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Multiparameter Eigenvalue Problems
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Author : Atkinson
language : en
Publisher: Academic Press
Release Date : 1972-06-16
Multiparameter Eigenvalue Problems written by Atkinson and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972-06-16 with Computers categories.
Multiparameter eigenvalue problems
Multiparameter Eigenvalue Problems
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Author : F. V. Atkinson
language : en
Publisher:
Release Date : 1972-01-01
Multiparameter Eigenvalue Problems written by F. V. Atkinson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972-01-01 with Eigenvalues categories.
Multiparameter Eigenvalue Problems And Expansion Theorems
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Author : Hans Volkmer
language : en
Publisher: Springer
Release Date : 2006-11-14
Multiparameter Eigenvalue Problems And Expansion Theorems written by Hans Volkmer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
This book provides a self-contained treatment of two of the main problems of multiparameter spectral theory: the existence of eigenvalues and the expansion in series of eigenfunctions. The results are first obtained in abstract Hilbert spaces and then applied to integral operators and differential operators. Special attention is paid to various definiteness conditions which can be imposed on multiparameter eigenvalue problems. The reader is not assumed to be familiar with multiparameter spectral theory but should have some knowledge of functional analysis, in particular of Brower's degree of maps.
Multiparameter Eigenvalue Problems
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Author : F.V. Atkinson
language : en
Publisher: CRC Press
Release Date : 2010-12-07
Multiparameter Eigenvalue Problems written by F.V. Atkinson and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-12-07 with Mathematics categories.
One of the masters in the differential equations community, the late F.V. Atkinson contributed seminal research to multiparameter spectral theory and Sturm-Liouville theory. His ideas and techniques have long inspired researchers and continue to stimulate discussion. With the help of co-author Angelo B. Mingarelli, Multiparameter Eigenvalue Problem
Multiparameter Eigenvalue Problems
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Author : Frederick V. Atkinson
language : en
Publisher:
Release Date : 1972
Multiparameter Eigenvalue Problems written by Frederick V. Atkinson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with Differential equations categories.
Multiparameter Eigenvalue Problems
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Author : F. V. Atkinson
language : en
Publisher:
Release Date : 1972
Multiparameter Eigenvalue Problems written by F. V. Atkinson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with Differential equations categories.
Multiparameter Eigenvalue Problems
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Author : Anders Källström
language : en
Publisher:
Release Date : 1977
Multiparameter Eigenvalue Problems written by Anders Källström and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977 with categories.
Multiparameter Eigenvalue Problems Methods And Algorithms
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Author : Bohdan Podlevskyi
language : en
Publisher:
Release Date : 2018-01-06
Multiparameter Eigenvalue Problems Methods And Algorithms written by Bohdan Podlevskyi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-06 with categories.
Multiparameter Eigenvalue Problems V 1 Matrices And Compact Operators
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Author : F. V. Atkinson
language : en
Publisher:
Release Date : 1972
Multiparameter Eigenvalue Problems V 1 Matrices And Compact Operators written by F. V. Atkinson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with categories.
Numerical Methods For Singular Multiparameter Eigenvalue Problems
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Author : Andrej Muhič
language : en
Publisher:
Release Date : 2011
Numerical Methods For Singular Multiparameter Eigenvalue Problems written by Andrej Muhič and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with categories.
In the 1960s Atkinson introduced an abstract algebraic setting for multiparameter eigenvalue problems. He showed that a nonsingular multiparameter eigenvalue problem is equivalent to the associated system of generalized eigenvalue problems. Many theoretical results and numerical methods for nonsingular multiparameter eigenvalue problems are based on this relation. We extend the above relation to singular two-parameter eigenvalue problems and show that the simple finite regular eigenvalues of a two-parameter eigenvalue problem and the common regular eigenvalues of the coupled generalized eigenvalue problem agree. Using the theory on the pencils of matrix polynomials we furthermore generalize the theory to the nonregular singular two-parameter eigenvalue problems. This enables one to solve a singular two-parameter eigenvalue problem by computing the common regular eigenvalues of the associated system of two singular generalized eigenvalue problems. There are various numerical methods for twoparameter eigenvalue problems, but all of them can only be applied to nonsingular problems. We develop a numerical method that can be applied to the singular two-parameter eigenvalue problems. It is based on the staircase algorithm for the extraction of the common regular part of two singular matrix pencils. We introduce the quadratic two-parameter eigenvalue problem (QMEP) and show that we can linearize it as a regular singular two-parameter eigenvalue problem. We present several transformations that can be used to solve the QMEP, by formulating an associated linear multiparameter eigenvalue problem. We also generalize the linearization to the polynomial twoparameter eigenvalue problem(PMEP). As an alternative approach to the linearization, we propose the transformation of the QMEP into a nonsingular five-parameter eigenvalue problem. We also consider several special cases of the QMEP, where some matrix coefficients are zero, which allows us to solve such QMEP more efficiently. We propose a Jacobi-Davidson type method for regular singular problems. We modify the Jacobi-Davidson type method for nonsingular two-parameter eigenvalue problem so that it can be applied to regular singular problems. The obtained algorithm can then be used to solve the problem obtained by linearizing the PMEP. If the dimension of matrices is large, then we cannot use the approach with linearization. If order of polynomials is small enough, then we can apply a Jacobi-Davidson type method directly to the polynomial system. This method is a generalization of the method for polynomial eigenvalue problems. We give some numerical results that illustrate the convergence of the introduced Jacobi-Davidson type methods.