Toeplitz Matrices, Asymptotic Linear Algebra, and Functional Analysis
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Author
Contributions
- Grudsky, Sergei M. - Contributor
Publication
2000 - Birkhäuser Basel, Basel, Switzerland
Language
English
Word Count
28,000 words, Guess
Page Count
112 pages
Physical Format
[electronic resource] /
Identifiers
- Open LibraryOL27092209M
- ISBN-139783034895484
- ISBN-103034895488
- OCLC Control Number851748758
Classifications
- DDC515
- LCCQA299.6-433
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.
Subjects
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