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Introduction to Large Truncated Toeplitz Matrices

  • Albrecht Böttcher
  • Bernd Silbermann

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Bernd Silbermann
    Pages 1-30
  3. Albrecht Böttcher, Bernd Silbermann
    Pages 31-58
  4. Albrecht Böttcher, Bernd Silbermann
    Pages 59-81
  5. Albrecht Böttcher, Bernd Silbermann
    Pages 83-119
  6. Albrecht Böttcher, Bernd Silbermann
    Pages 121-183
  7. Albrecht Böttcher, Bernd Silbermann
    Pages 185-219
  8. Albrecht Böttcher, Bernd Silbermann
    Pages 221-241
  9. Back Matter
    Pages 243-259

About this book

Introduction

Introduction to Large Truncated Toeplitz Matrices is a text on the application of functional analysis and operator theory to some concrete asymptotic problems of linear algebra. The book contains results on the stability of projection methods, deals with asymptotic inverses and Moore-Penrose inversion of large Toeplitz matrices, and embarks on the asymptotic behavoir of the norms of inverses, the pseudospectra, the singular values, and the eigenvalues of large Toeplitz matrices. The approach is heavily based on Banach algebra techniques and nicely demonstrates the usefulness of C*-algebras and local principles in numerical analysis. The book includes classical topics as well as results obtained and methods developed only in the last few years. Though employing modern tools, the exposition is elementary and aims at pointing out the mathematical background behind some interesting phenomena one encounters when working with large Toeplitz matrices. The text is accessible to readers with basic knowledge in functional analysis. It is addressed to graduate students, teachers, and researchers with some inclination to concrete operator theory and should be of interest to everyone who has to deal with infinite matrices (Toeplitz or not) and their large truncations.

Keywords

Algebra Banach algebra Distribution Eigenvalue Matrix Operator theory Sage functional analysis linear algebra

Authors and affiliations

  • Albrecht Böttcher
    • 1
  • Bernd Silbermann
    • 1
  1. 1.Fakultät für MathematikTechnische Universität ChemnitzChemnitzGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-1426-7
  • Copyright Information Springer-Verlag New York, Inc. 1999
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-7139-0
  • Online ISBN 978-1-4612-1426-7
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • Buy this book on publisher's site