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Full Description
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.
Contents
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
