A best upper bound for the 2-norm condition number of a matrix

被引：31

作者：

Merikoski, JK ^{[1
]}

Urpala, U ^{[1
]}

Virtanen, A ^{[1
]}

Tam, TY ^{[1
]}

Uhlig, F ^{[1
]}

机构：

[1] AUBURN UNIV, DEPT MATH, AUBURN, AL 36849 USA

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 1997年 / 254卷

关键词：

D O I：

10.1016/S0024-3795(96)00474-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 [应用数学];

摘要：

Let A be an n x n nonsingular real or complex matrix. The best possible upper bound for the ratio of the largest and smallest singular values of A, using tr A*A, det A, and n only, is obtained. A comparison with an earlier bound is given, and the singular and nonsquare cases are included. If all the eigenvalues of A are real and positive, the best possible upper bound for the ratio of the largest and smallest eigenvalues of A, involving tr A, det A, and n only, is presented as well. (C) Elsevier Science Inc., 1997.

引用

页码：355 / 365

页数：11