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Toeplitz Matrices, Asymptotic Linear Algebra, and Functional Analysis

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Published by Birkhäuser Basel, Imprint: Birkhäuser in Basel .
Written in English

Subjects:

  • Mathematics,
  • Global analysis (Mathematics)

Book details:

About the Edition

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.

Edition Notes

Statementby Albrecht Böttcher, Sergei M. Grudsky
ContributionsGrudsky, Sergei M.
Classifications
LC ClassificationsQA299.6-433
The Physical Object
Format[electronic resource] /
Pagination1 online resource (x, 112 p.)
Number of Pages112
ID Numbers
Open LibraryOL27092209M
ISBN 103034895488, 3034883951
ISBN 109783034895484, 9783034883955
OCLC/WorldCa851748758

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A Toeplitz matrix may be defined as a matrix A where A i,j = c i−j, for constants c 1−n c n−1. The set of n×n Toeplitz matrices is a subspace of the vector space of n×n matrices under matrix addition and scalar multiplication. Two Toeplitz matrices may be added in O time and multiplied in O(n 2) time. Toeplitz matrices are persymmetric. This text offers an introduction to some problems of Toeplitz matrices that are placed in the borderland between linear algebra and functional analysis. The author's confine themselves to Toeplitz matrices with rational symbols, and focus on the asymptotic behaviour of the singular values. 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. Instant download; Readable on all devices; Own it forever; Local sales tax included if applicable.

Dec 01,  · A. Böttcher and S.M. Grudsky:Toeplitz Matrices, Asymptotic Linear Algebra, and Functional Analysis. Hindustan Book Agency, New Delhi and Birkhäuser Verlag, Basel Hindustan Book Agency, New Delhi and Birkhäuser Verlag, Basel Cited by: Literature 1.A. B¨ottcher, S. Grudsky. Toeplitz Matrices, Asymptotic Linear Algebra, and Functional Analysis. Hindustan Book Agency, New Delhi, and Birkh¨auser. Applying functional analysis and operator theory to some concrete asymptotic problems of linear algebra, this 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 behaviour of the norms of inverses, the pseudospectra, the singular values, and the eigenvalues of large Cited by: 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.

In operator theory, a Toeplitz operator is the compression of a multiplication operator on the circle to the Hardy space.. Details. Let S 1 be the circle, with the standard Lebesgue measure, and L 2 (S 1) be the Hilbert space of square-integrable functions.A bounded measurable function g on S 1 defines a multiplication operator M g on L 2 (S 1).Let P be the projection from L 2 (S 1) onto the. Applying functional analysis and operator theory to some concrete asymptotic problems of linear algebra, this 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 behaviour of the norms of inverses, the pseudospectra. Toeplitz Matrices, Asymptotic Linear Algebra, and Functional Analysis的话题 · · · · · · (全部 条) 什么是话题 无论是一部作品、一个人,还是一件事,都往往可以衍生出许多不同的话题。. Product Information. Applying functional analysis and operator theory to some concrete asymptotic problems of linear algebra, this 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 behaviour of the norms of inverses, the pseudospectra, the singular values, and the.