Numerical Methods for Eigenvalue Problems

Steffen Börm; Christian Mehl

Published by De Gruyter 2012

Numerical Methods for Eigenvalue Problems

Steffen Börm and Christian Mehl

In the series De Gruyter Textbook

https://doi.org/10.1515/9783110250374

Overview
Contents

About this book

Eigenvalues and eigenvectors of matrices and linear operators play an important role when solving problems from structural mechanics and electrodynamics, e.g., by describing the resonance frequencies of systems, when investigating the long-term behavior of stochastic processes, e.g., by describing invariant probability measures, and as a tool for solving more general mathematical problems, e.g., by diagonalizing ordinary differential equations or systems from control theory.

This textbook presents a number of the most important numerical methods for finding eigenvalues and eigenvectors of matrices. The authors discuss the central ideas underlying the different algorithms and introduce the theoretical concepts required to analyze their behavior with the goal to present an easily accessible introduction to the field, including rigorous proofs of all important results, but not a complete overview of the vast body of research. Several programming examples allow the reader to experience the behavior of the different algorithms first-hand.

The book addresses students and lecturers of mathematics, physics and engineering who are interested in the fundamental ideas of modern numerical methods and want to learn how to apply and extend these ideas to solve new problems.

Appropriate as a textbook for graduate courses or for independent study
Several exercises and summaries of each chapter help beginners to understand the material
Source codes of the presented algorithms available online

Author / Editor information

Steffen Börm, Christian-Albrechts-Universität zu Kiel, Germany; Christian Mehl, Technische Universität Berlin, Germany.

Reviews

„Hinreichend ausführliche und gut verständliche Beweise."
Prof. Dr. Alexander Hornberg, Hochschule Esslingen

Topics

Frontmatter Requires Authentication Unlicensed Licensed Download PDF	i
Preface Requires Authentication Unlicensed Licensed Download PDF	v
Contents Requires Authentication Unlicensed Licensed Download PDF	vii
Chapter 1. Introduction Requires Authentication Unlicensed Licensed Download PDF	1
Chapter 2. Existence and properties of eigenvalues and eigenvectors Requires Authentication Unlicensed Licensed Download PDF	8
Chapter 3. Jacobi iteration Requires Authentication Unlicensed Licensed Download PDF	39
Chapter 4. Power methods Requires Authentication Unlicensed Licensed Download PDF	61
Chapter 5. QR iteration Requires Authentication Unlicensed Licensed Download PDF	100
Chapter 6. Bisection methods Requires Authentication Unlicensed Licensed Download PDF	132
Chapter 7. Krylov subspace methods for large sparse eigenvalue problems Requires Authentication Unlicensed Licensed Download PDF	145
Chapter 8. Generalized and polynomial eigenvalue problems Requires Authentication Unlicensed Licensed Download PDF	182
Bibliography Requires Authentication Unlicensed Licensed Download PDF	203
Index Requires Authentication Unlicensed Licensed Download PDF	206

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Students and Lecturers in Mathematics and Engineering; Academic Libraries
Pages
- Front matter: 8
- Main content: 208
Illustrations
- Coloured Illustrations: 20
Keywords: Eigenvalue Problem; Jacobi Iteration; Vector Iteration; QR Iteration; Bisection Method

eBook

Published: May 29, 2012
ISBN: 9783110250374

Hardcover

Published: May 30, 2012
ISBN: 9783110250336