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9780898715996 Academic Inspection Copy

Spectral Properties of Banded Toeplitz Matrices

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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, Spectral Properties of Banded Toeplitz Matrices is an important resource. 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 a text for introducing the material and as a reference. The approach is based on the know-how and experience of the authors in combining functional analytical methods with hard analysis and in applying operator theoretical methods to matrix theory, which reveals the essence of several phenomena and leads to significant improvements in existing results. All basic results presented in the book are precisely stated as theorems and accompanied by full proofs.
Preface Chapter 1: Infinite Matrices Chapter 2: Determinants Chapter 3: Stability Chapter 4: Instability Chapter 5: Norms Chapter 6: Condition Numbers Chapter 7: Substitutes for the Spectrum Chapter 8: Transient Behavior Chapter 9: Singular Values Chapter 10: Extreme Eigenvalues Chapter 11: Eigenvalue Distribution Chapter 12: Eigenvectors and Pseudomodes Chapter 13: Structured Perturbations Chapter 14: Impurities Bibliography Index
'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
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