
Toeplitz Matrices, Asymptotic Linear Algebra, and Functional Analysis
Birkhäuser (Publisher)
Published on 5. November 2012
Book
Paperback/Softback
X, 112 pages
978-3-0348-9548-4 (ISBN)
Description
The subject of this text is the relation between the properties of infinite Toeplitz matrices ao a_I a_2 al ao a_I a2 al ao and their large finite sections This is very big and even inexhaustible subject, and therefore we must limit ourselves to a few concrete problems here. We will focus our attention on singular values. The singular values of An are the eigenvalues of (A~An)I/2. The properties of the singular values of An for fixed n (or, as in so-called interlacing theorems, for some consecutive n) are studied in linear algebra. The problem of determining the singular values of An for large n (say n = 700) is a business of numerical linear algebra. The behavior of the singular 23 values of An for n --+ 00 (or, say, for n = 10 ) is a concern of asymptotic linear algebra. Finally, the investigation of the properties of the infinite matrix A is a task of functional analysis. To get an idea of what this text is about, we cite a few questions we will consider. Preface viii Question 1. Does the smallest singular value 81 (An) stay away from zero as n -t oo? Because this is the question whether the norms IIA;;111 are uniformly bounded for all sufficiently large n.
More details
Edition
2000
Language
English
Place of publication
Basel
Switzerland
Publishing group
Springer Basel
Target group
Professional and scholarly
Lower undergraduate
Illustrations
X, 112 p.
Dimensions
Height: 24 cm
Width: 17 cm
Weight
223 gr
ISBN-13
978-3-0348-9548-4 (9783034895484)
DOI
10.1007/978-3-0348-8395-5
Schweitzer Classification
Other editions
Additional editions

Albrecht Böttcher | Sergei M. Grudsky
Toeplitz Matrices, Asymptotic Linear Algebra, and Functional Analysis
Book
06/2000
1st Edition
Springer
€42.75
Article exhausted; check different version
Content
1 Infinite Toeplitz Matrices.- 2 C*-Algebras in Action.- 3 Instability.- 4 Condition Numbers.- 5 Singular Values.- Notation Index.