On the condition numbers of large semi-definite Toeplitz matrices

被引：62

作者：

Bottcher, A ^{[1
]}

Grudsky, SM

机构：

[1] TU Chemnitz, Fak Math, D-09107 Chemnitz, Germany

[2] Rostov Don State Univ, Fac Mech & Math, Rostov 344711, Russia

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 1998年 / 279卷 / 1-3期

关键词：

condition number; singular value Toeplitz matrix;

D O I：

10.1016/S0024-3795(98)00015-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is devoted to asymptotic estimates for the (spectral or Euclidean) condition numbers kappa(T-n(a)) = \\T-n(a)\\ \\T-n(-1)(a)\\ of large n x n Toeplitz matrices T-n(a) in the case where the symbol a is an L-infinity function and Re a greater than or equal to 0 almost everywhere. We describe several classes of symbols n for which kappa(T-n(a)) increases like (log n)(alpha), n(alpha), or even e(alpha n). (C) 1998 Elsevier Science Inc. All rights reserved.

引用

页码：285 / 301

页数：17

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