Comment on "condition number of Drazin inverse and their condition numbers of singular linear systems''

被引：3

作者：

Chen, Jueping ^{[2
,3
]}

Xu, Zhaoliang ^{[1
]}

机构：

[1] Shanghai Maritime Univ, Dept Math, Shanghai 200135, Peoples R China

[2] Fudan Univ, Sch Math Sci, Inst Math, Shanghai 200433, Peoples R China

[3] Fudan Univ, Minist Educ, Key Lab Math Nonlinear Sci, Shanghai, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2008年 / 199卷 / 02期

基金：

中国国家自然科学基金;

关键词：

condition number; Drazin inverse; perturbation; index; Schur decomposition;

D O I：

10.1016/j.amc.2007.10.008

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we establish the condition number of Drazin inverse of a singular matrix A, where R(A(k)) = R(A(k*)) and k = index(A), by the Schur decomposition. Based on this form, the spectral norm and Frobenius norm of relative condition number for the Drazin inverse and level-2 condition number of the Drazin inverse are characterized. The sensitivity for the Drazin-inverse solution of singular systems is also presented. We obtain several formulas for the condition number of the Drazin inverse by spectral norm instead of the P-norm, where P is a transformation matrix of the Jordan canonical form of A, thereby improving the earlier work [Y. Wei, G. Wang, D. Wang, Condition number of Drazin inverse and their condition numbers of singular linear systems, Appl. Math. Comput. 146 (2003) 455-467]. (c) 2007 Elsevier Inc. All rights reserved.

引用

页码：512 / 526

页数：15

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