Spectral Properties of Banded Toeplitz Matrices
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Author(s): A. Böttcher and S. Grudsky
Publisher: SIAM
ISBN: 0898715997
Format: softback
411pp
Price: $95.00
Review Date: 07 December 2005
Review: This book provides an introduction to the behaviour of several spectral characteristics of large Toeplitz band matrices. The spectral characteristics include determinants, eigenvalues and eigenvectors, pseudspectra and pseudomodes, singular values, norms, and condition numbers. The text is based on the knowledge and experience of the authors in combining functional analytical methods with hard analysis and in applying operator theoretical methods to matrix theory, which exposes the essence of several phenomena and leads to significant improvements in existing results. There are chapters on: infinite matrices; determinants; stability; instability; norms; condition numbers; substitutes for the spectrum; transient behaviour; singular values; extreme eigenvalues; eigenvalues distribution; eigenvectors and pseudomodes; structured perturbations; and impurities.