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Börm, Steffen / Mehl, Christian

Numerical Methods for Eigenvalue Problems

Series:De Gruyter Textbook

    300,00 € / $420.00 / £272.50*

    eBook (PDF)
    Publication Date:
    May 2012
    Copyright year:
    2012
    ISBN
    978-3-11-025037-4
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    Overview

    • 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

    Aims and Scope

    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.

    Details

    viii, 208 pages
    Language:
    English
    Type of Publication:
    Textbook
    Keyword(s):
    Eigenvalue Problem; Jacobi Iteration; Vector Iteration; QR Iteration; Bisection Method

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    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

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