On the condition numbers of large semi-definite Toeplitz matrices

被引：60
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.
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页码：285 / 301
页数：17
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