Toeplitz Matrices, Asymptotic Linear Algebra, and Functional Analysis
By: by Albrecht Böttcher, Sergei M. Grudsky
Contributors: Grudsky, Sergei M.
Publisher: Birkhäuser Basel; Imprint: Birkhäuser
Published: 2000
Place of publication: Basel
Language: eng
Format: [electronic resource] /
Number of pages: 112
ISBN-13: 9783034895484; 9783034883955
Subjects: Mathematics; Global analysis (Mathematics)
Description: 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.
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