Toeplitz Matrices, Asymptotic Linear Algebra, and Functional Analysis / Edition 1

Toeplitz Matrices, Asymptotic Linear Algebra, and Functional Analysis / Edition 1

by Albrecht Bottcher, Sergei M. Grudsky
     
 

ISBN-10: 3764362901

ISBN-13: 9783764362904

Pub. Date: 07/28/2000

Publisher: Springer-Verlag New York, LLC

This text is a self-contained introduction to some problems for Toeplitz matrices that are placed in the borderland between linear algebra and functional analysis. The text looks at Toeplitz matrices with rational symbols, and focuses attention on the asymptotic behavior of the singular values, which includes the behavior of the norms, the norms of the inverses, and…  See more details below

Overview

This text is a self-contained introduction to some problems for Toeplitz matrices that are placed in the borderland between linear algebra and functional analysis. The text looks at Toeplitz matrices with rational symbols, and focuses attention on the asymptotic behavior of the singular values, which includes the behavior of the norms, the norms of the inverses, and the condition numbers as special cases. The text illustrates that the asymptotics of several linear algebra characteristics depend in a fascinating way on functional analytic properties of infinite matrices. Many convergence results can very comfortably be obtained by working with appropriate C*-algebras, while refinements of these results, for example, estimates of the convergence speed, nevertheless require hard analysis.

Product Details

ISBN-13:
9783764362904
Publisher:
Springer-Verlag New York, LLC
Publication date:
07/28/2000
Pages:
128
Product dimensions:
9.61(w) x 6.69(h) x 0.27(d)

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