Author: Xuefeng Liu
Publisher: Springer Nature
ISBN: 9819735777
Category :
Languages : en
Pages : 139
Book Description
Guaranteed Computational Methods for Self-Adjoint Differential Eigenvalue Problems
Author: Xuefeng Liu
Publisher: Springer Nature
ISBN: 9819735777
Category :
Languages : en
Pages : 139
Book Description
Publisher: Springer Nature
ISBN: 9819735777
Category :
Languages : en
Pages : 139
Book Description
Numerical Solution of a Non-self-adjoint Differential Eigenvalue Problem
Author: H. Bruun Nielsen
Publisher:
ISBN:
Category :
Languages : en
Pages : 29
Book Description
Publisher:
ISBN:
Category :
Languages : en
Pages : 29
Book Description
High-Precision Methods in Eigenvalue Problems and Their Applications
Author: Leonid D. Akulenko
Publisher: CRC Press
ISBN: 020340128X
Category : Science
Languages : en
Pages : 261
Book Description
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
Publisher: CRC Press
ISBN: 020340128X
Category : Science
Languages : en
Pages : 261
Book Description
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
Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations
Author: Mitsuhiro T. Nakao
Publisher: Springer Nature
ISBN: 9811376697
Category : Mathematics
Languages : en
Pages : 469
Book Description
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.
Publisher: Springer Nature
ISBN: 9811376697
Category : Mathematics
Languages : en
Pages : 469
Book Description
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.
Refined Iterative Methods for Computation of the Solution and the Eigenvalues of Self-Adjoint Boundary Value Problems
Author: M. Engeli
Publisher: Birkhauser
ISBN: 9780817600983
Category :
Languages : en
Pages : 108
Book Description
Publisher: Birkhauser
ISBN: 9780817600983
Category :
Languages : en
Pages : 108
Book Description
Numerical Methods for Large Eigenvalue Problems
Author: Yousef Saad
Publisher: SIAM
ISBN: 9781611970739
Category : Mathematics
Languages : en
Pages : 292
Book Description
This revised edition discusses numerical methods for computing eigenvalues and eigenvectors of large sparse matrices. It provides an in-depth view of the numerical methods that are applicable for solving matrix eigenvalue problems that arise in various engineering and scientific applications. Each chapter was updated by shortening or deleting outdated topics, adding topics of more recent interest, and adapting the Notes and References section. Significant changes have been made to Chapters 6 through 8, which describe algorithms and their implementations and now include topics such as the implicit restart techniques, the Jacobi-Davidson method, and automatic multilevel substructuring.
Publisher: SIAM
ISBN: 9781611970739
Category : Mathematics
Languages : en
Pages : 292
Book Description
This revised edition discusses numerical methods for computing eigenvalues and eigenvectors of large sparse matrices. It provides an in-depth view of the numerical methods that are applicable for solving matrix eigenvalue problems that arise in various engineering and scientific applications. Each chapter was updated by shortening or deleting outdated topics, adding topics of more recent interest, and adapting the Notes and References section. Significant changes have been made to Chapters 6 through 8, which describe algorithms and their implementations and now include topics such as the implicit restart techniques, the Jacobi-Davidson method, and automatic multilevel substructuring.
Numerical Methods for General and Structured Eigenvalue Problems
Author: Daniel Kressner
Publisher: Springer Science & Business Media
ISBN: 3540285024
Category : Mathematics
Languages : en
Pages : 272
Book Description
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.
Publisher: Springer Science & Business Media
ISBN: 3540285024
Category : Mathematics
Languages : en
Pages : 272
Book Description
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.
Computational Methods in Structural Dynamics
Author: L. Meirovitch
Publisher: Springer Science & Business Media
ISBN: 9789028605800
Category : Mathematics
Languages : en
Pages : 462
Book Description
Publisher: Springer Science & Business Media
ISBN: 9789028605800
Category : Mathematics
Languages : en
Pages : 462
Book Description
Bounds for the Eigenvalues of a Matrix
Author: Kenneth R. Garren
Publisher:
ISBN:
Category : Eigenvalues
Languages : en
Pages : 52
Book Description
Publisher:
ISBN:
Category : Eigenvalues
Languages : en
Pages : 52
Book Description
Computational Techniques for Differential Equation Eigenvalue Problems on Vector Processors
Author: David L. Harrar
Publisher:
ISBN:
Category : Bifurcation theory
Languages : en
Pages : 29
Book Description
Publisher:
ISBN:
Category : Bifurcation theory
Languages : en
Pages : 29
Book Description