On level-2 condition number for the weighted Moore-Penrose inverse

被引：10

作者：

Lin, Lijing ^{[2
]}

Lu, Tzon-Tzer ^{[3
]}

Wei, Yimin ^{[1
,4
]}

机构：

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

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

[3] Natl Sun Yat Sen Univ, Dept Appl Math, Kaohsiung 80424, Taiwan

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

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2008年 / 55卷 / 04期

基金：

中国国家自然科学基金;

关键词：

weighted Moore-Penrose inverse; condition number; level-2 condition number; perturbation; weighted linear least squares problem;

D O I：

10.1016/j.camwa.2007.06.005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we present characterizations for the level-2 condition number of the weighted Moore-Penrose inverse, i.e., cond(MN)(A) <= cond(MN)([2]) (A) <= cond(MN)(A) 1. where cond(MN)(A) is the condition number of the weighted Moore-Penrose inverse of a rectangular matrix and cond(MN)([2])(A) is the level-2 condition number of this problem. This paper extends the result by Cucker, Diao and Wei [F. Cucker, H. Diao, Y. Wei, On the level-2 condition number for Moore-Penrose inversion, 2005, Unpublished report] and improves the results by Wei and Wang [Y. Wei, D. Wang, Condition numbers and perturbation of weighted Moore-Penrose inverse and weighted linear least squares problem, Appl. Math. Comput. 145 (2003) 45-58]. (c) 2007 Elsevier Ltd. All rights reserved.

引用

页码：788 / 800

页数：13

共 27 条

[1]

Ben-Israel A., 2003, GEN INVERSES THEORY, V15

[2] A note on level-2 condition numbers [J].

Cheung, D ;

Cucker, F .

JOURNAL OF COMPLEXITY, 2005, 21 (03) :314-319

[3] Smoothed analysis of some condition numbers [J].

Cucker, F ;

Diao, H ;

Wei, Y .

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, 2006, 13 (01) :71-84

[4]

CUCKER F, 2005, UNPUB LEVEL 2 CONDIT

[5] On mixed and componentwise condition numbers for Moore-Penrose inverse and linear least squares problems [J].

Cucker, Felipe ;

Diao, Huaian ;

Wei, Yimin .

MATHEMATICS OF COMPUTATION, 2007, 76 (258) :947-963

[6] ON CONDITION NUMBERS AND THE DISTANCE TO THE NEAREST ILL-POSED PROBLEM [J].

DEMMEL, JW .

NUMERISCHE MATHEMATIK, 1987, 51 (03) :251-289

[7]

Golub G. H., 1996, MATRIX COMPUTATIONS

[8] On the condition number of linear least squares problems in a weighted Frobenius norm [J].

Gratton, S .

BIT NUMERICAL MATHEMATICS, 1996, 36 (03) :523-530

[9] Perturbation bounds for constrained and weighted least squares problems [J].

Gulliksson, M ;

Jin, XQ ;

Wei, YM .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2002, 349 :221-232

[10] Perturbation identities for regularized Tikhonov inverses and weighted pseudoinverses [J].

Gulliksson, ME ;

Wedin, PÅ ;

Wei, YM .

BIT NUMERICAL MATHEMATICS, 2000, 40 (03) :513-523

← 1 2 3 →