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

Authors:
Lijing Lin;Tzon-Tzer Lu;Yimin Wei
Affiliations:
Institute of Mathematics, Fudan University, Shanghai, 200433, PR China;Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, 80424, Taiwan;Institute of Mathematics, School of Mathematical Sciences, Fudan University, Shanghai, 200433, PR China and Key Laboratory of Nonlinear Science (Fudan University), Education of Ministry, PR China
Venue:
Computers & Mathematics with Applications
Year:
2008

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Abstract

In this paper, we present characterizations for the level-2 condition number of the weighted Moore-Penrose inverse, i.e., cond"M"N(A)@?cond"M"N^[^2^](A)@?cond"M"N(A)+1, where cond"M"N(A) is the condition number of the weighted Moore-Penrose inverse of a rectangular matrix and cond"M"N^[^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by Cucker, Diao and Wei [F. Cucker, H. Diao, Y. Wei, On the level-2 condition number for Moore-Penrose inversion, 2005, Unpublished report] and improves the results by Wei and Wang [Y. Wei, D. Wang, Condition numbers and perturbation of weighted Moore-Penrose inverse and weighted linear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].