Condition number for the Drazin inverse and the Drazin-inverse solution of singular linear system with their condition numbers

Authors:
Yimin Wei;Huaian Diao
Affiliations:
Department of Mathematics, Fudan University, Shanghai, 200433, PR China;Department of Mathematics, City University of Hong Kong, Hong Kong, PR China and Institute of Mathematics, Fudan University, Shanghai, 200433, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2005

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Abstract

In this paper, we investigate the condition number of Drazin inverse and Drazin-inverse solution of singular linear system Ax = b, where A is a n × n rank-deficient matrix and b a real vector of size n, x a real vector. Let α and β be two positive real numbers, when we consider the weighted Frobenius norm ||[αA, βb]||P,Q(F) on the data we get the formula of condition number of the Drazin-inverse solution of singular linear system. For the normwise condition number, the sensitivity of the relative condition number itself is studied, the componentwise perturbation is also investigated.