Guaranteed Computational Methods For Self Adjoint Differential Eigenvalue Problems

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Guaranteed Computational Methods For Self Adjoint Differential Eigenvalue Problems

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Author : Xuefeng Liu
language : en
Publisher: Springer Nature
Release Date :

Guaranteed Computational Methods For Self Adjoint Differential Eigenvalue Problems written by Xuefeng Liu and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.

Numerical Solution Of A Non Self Adjoint Differential Eigenvalue Problem

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Author : H. Bruun Nielsen
language : en
Publisher:
Release Date : 1977

Numerical Solution Of A Non Self Adjoint Differential Eigenvalue Problem written by H. Bruun Nielsen 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.

High Precision Methods In Eigenvalue Problems And Their Applications

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Author : Leonid D. Akulenko
language : en
Publisher: CRC Press
Release Date : 2004-10-15

High Precision Methods In Eigenvalue Problems And Their Applications written by Leonid D. Akulenko and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-10-15 with Science categories.

This book presents a survey of analytical, asymptotic, numerical, and combined methods of solving eigenvalue problems. It considers the new method of accelerated convergence for solving problems of the Sturm-Liouville type as well as boundary-value problems with boundary conditions of the first, second, and third kind. The authors also present high

Refined Iterative Methods For Computation Of The Solution And The Eigenvalues Of Self Adjoint Boundary Value Problems

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Author : M. Engeli
language : en
Publisher: Birkhauser
Release Date : 1980-01-01

Refined Iterative Methods For Computation Of The Solution And The Eigenvalues Of Self Adjoint Boundary Value Problems written by M. Engeli and has been published by Birkhauser this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980-01-01 with categories.

Numerical Verification Methods And Computer Assisted Proofs For Partial Differential Equations

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Author : Mitsuhiro T. Nakao
language : en
Publisher: Springer Nature
Release Date : 2019-11-11

Numerical Verification Methods And Computer Assisted Proofs For Partial Differential Equations written by Mitsuhiro T. Nakao and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-11 with Mathematics categories.

In the last decades, various mathematical problems have been solved by computer-assisted proofs, among them the Kepler conjecture, the existence of chaos, the existence of the Lorenz attractor, the famous four-color problem, and more. In many cases, computer-assisted proofs have the remarkable advantage (compared with a “theoretical” proof) of additionally providing accurate quantitative information. The authors have been working more than a quarter century to establish methods for the verified computation of solutions for partial differential equations, mainly for nonlinear elliptic problems of the form -∆u=f(x,u,∇u) with Dirichlet boundary conditions. Here, by “verified computation” is meant a computer-assisted numerical approach for proving the existence of a solution in a close and explicit neighborhood of an approximate solution. The quantitative information provided by these techniques is also significant from the viewpoint of a posteriori error estimates for approximate solutions of the concerned partial differential equations in a mathematically rigorous sense. In this monograph, the authors give a detailed description of the verified computations and computer-assisted proofs for partial differential equations that they developed. In Part I, the methods mainly studied by the authors Nakao and Watanabe are presented. These methods are based on a finite dimensional projection and constructive a priori error estimates for finite element approximations of the Poisson equation. In Part II, the computer-assisted approaches via eigenvalue bounds developed by the author Plum are explained in detail. The main task of this method consists of establishing eigenvalue bounds for the linearization of the corresponding nonlinear problem at the computed approximate solution. Some brief remarks on other approaches are also given in Part III. Each method in Parts I and II is accompanied by appropriate numerical examples that confirm the actual usefulness of the authors’ methods. Also in some examples practical computer algorithms are supplied so that readers can easily implement the verification programs by themselves.

An Optimal Method Of Computing The Eigenvalues Of The Selfadjoint Eigenvalue Problem For The Ordinary Differential Equations

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Author : Teresa Regińska
language : en
Publisher:
Release Date : 1970

An Optimal Method Of Computing The Eigenvalues Of The Selfadjoint Eigenvalue Problem For The Ordinary Differential Equations written by Teresa Regińska and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with categories.

Novel Computational Methods For Eigenvalue Problems

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Author :
language : en
Publisher:
Release Date : 2019

Novel Computational Methods For Eigenvalue Problems written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with categories.

Abstract : This dissertation focuses on novel computational method for eigenvalue problems. In Chapter 1, preliminaries of functional analysis related to eigenvalue problems are presented. Some classical methods for matrix eigenvalue problems are discussed. Several PDE eigenvalue problems are covered. The chapter is concluded with a summary of the contributions. In Chapter 2, a novel recursive contour integral method (RIM) for matrix eigenvalue problem is proposed. This method can effectively find all eigenvalues in a region on the complex plane with no a priori spectrum information. Regions that contain eigenvalues are subdivided and tested recursively until the size of region reaches specified precision. The method is robust, which is demonstrated using various examples. In Chapter 3, we propose an improved version of RIM for non-Hermitian eigenvalue problems, called SIM-M. By incorporating Cayley transformation and Arnoldi's method, the main computation cost of solving linear systems is reduced significantly. The numerical experiments demonstrate that RIM-M gains significant speed-up over RIM. In Chapter 4, we propose a multilevel spectral indicator method (SIM-M) to address the memory requirement for large sparse matrices. We modify the indicator of RIM-M such that it requires much less memory. Matrices from University of Florida Sparse Matrix Collection are tested, suggesting that a parallel version of SIM-M has the potential to be efficient. In Chapter 5, we develop a novel method to solve the elliptic PDE eigenvalue problem. We construct a multi-wavelet basis with Riesz stability in H1 0 ( ). By incorporating multi-grid discretization scheme and sparse grids, the method retains the optimal convergence rate for the smallest eigenvalue with much less computational cost.

Numerical Methods For General And Structured Eigenvalue Problems

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Author : Daniel Kressner
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-01-20

Numerical Methods For General And Structured Eigenvalue Problems written by Daniel Kressner and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-20 with Mathematics categories.

This book is about computing eigenvalues, eigenvectors, and invariant subspaces of matrices. Treatment includes generalized and structured eigenvalue problems and all vital aspects of eigenvalue computations. A unique feature is the detailed treatment of structured eigenvalue problems, providing insight on accuracy and efficiency gains to be expected from algorithms that take the structure of a matrix into account.

A Method For Approximating The Eigenvalues Of Non Self Adjoint Ordinary Differential Operators

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Author : John E. Osborn
language : en
Publisher:
Release Date : 1979

A Method For Approximating The Eigenvalues Of Non Self Adjoint Ordinary Differential Operators written by John E. Osborn and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Differential operators categories.

Computational Techniques For Differential Equation Eigenvalue Problems On Vector Processors

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Author : David L. Harrar
language : en
Publisher:
Release Date : 1999

Computational Techniques For Differential Equation Eigenvalue Problems On Vector Processors written by David L. Harrar and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Bifurcation theory categories.