Spectral Properties of Banded Toeplitz Matrices
Spectral Properties of Banded Toeplitz Matrices
Sergei M. Grudsky
This self-contained introduction to the behavior of several spectral characteristics of large Toeplitz band matrices is the first systematic presentation of a relatively large body of knowledge, covering everything from classic results to the most recent developments. The spectral characteristics include determinants, eigenvalues and eigenvectors, pseudospectra and pseudomodes, singular values, norms, and condition numbers. Toeplitz matrices emerge in many applications and the literature on them is immense. They remain an active field of research with many facets, and the material on banded ones until now has primarily been found in research papers. The book may serve both as an introductory text and as a reference. The approach is based on the experience of the authors in combining functional analytical methods with hard analysis, and in applying operator theoretical methods to matrix theory, revealing the essence of several phenomena and leading to significant improvements in existing results.
- All basic results presented in the book are precisely stated and come with full proofs
- Covers much material previously unavailable in book form
- Can be used for self-teaching or as a reference
Reviews & endorsements
'This is a wonderful book, full of the latest material on Toeplitz matrices and operators, including norms, spectra, pseudospectra, fields of values, and polynomial hulls. The notes at the end of the chapters are especially interesting and the exercises are challenging. The writing is careful and precise but also entertaining.' Anne Greenbaum, Professor of Mathematics, University of Washington
'This book is a tremendous resource for all aspects of the spectral theory of banded Toeplitz matrices. It will be the first place I turn when looking for many results in this field, and given this book's amazing breadth and depth, I expect to find just what I need.' Mark Embree, Assistant Professor of Computational and Applied Mathematics, Rice University
Product details
December 2005Paperback
9780898715996
421 pages
254 × 175 × 23 mm
0.733kg
This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
Table of Contents
- Preface
- 1. Infinite matrices
- 2. Determinants
- 3. Stability
- 4. Instability
- 5. Norms
- 6. Condition numbers
- 7. Substitutes for the spectrum
- 8. Transient behavior
- 9. Singular values
- 10. Extreme eigenvalues
- 11. Eigenvalue distribution
- 12. Eigenvectors and pseudomodes
- 13. Structured perturbations
- 14. Impurities
- Bibliography
- Index.
