Introduction to Large Truncated Toeplitz Matrices
By: by Albrecht Böttcher, Bernd Silbermann
Contributors: Silbermann, Bernd
Series: Universitext; Universitext
Publisher: Springer New York
Published: 1999
Place of publication: New York, NY
Language: eng
Format: [electronic resource] /
Number of pages: 259
ISBN-13: 9781461271390; 9781461214267
Subjects: Mathematics; Global analysis (Mathematics); Matrix theory; Topology
Description: 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.
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Table of contents: title: Preface; title: Infinite matrices; title: Finite section method and stability; title: Norms of inverses and pseudospectra; title: Moore-Penrose inverses and singular values; title: Determinants and eigenvalues; title: Block Toeplitz matrices; title: Banach space phenomena; title: Bibliography and Index.