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

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 x n rank-deficient matrix and b a real vector of size n,x a real vector. Let alpha and beta be two positive real numbers, when we consider the weighted Frobenius norm parallel to[alpha A,beta b]parallel to((F))(P,Q) 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. (c) 2004 Elsevier B.V. All rights reserved.