• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.35-59
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• 2006

In this paper, we generalized the results of [23, 26], and get the results of the condition number of the W-weighted Drazin-inverse solution of linear system W AW\chi=b, where A is an $m{\times}n$ rank-deficient matrix and the index of A W is $k_1$, the index of W A is $k_2$, b is a real vector of size n in the range of $(WA)^{k_2}$, $\chi$ is a real vector of size m in the range of $(AW)^{k_1}$. Let $\alpha$ and $\beta$ be two positive real numbers, when we consider the weighted Frobenius norm $\|[{\alpha}W\;AW,\;{\beta}b]\|$(equation omitted) on the data we get the formula of condition number of the W-weighted Drazin-inverse solution of linear system. For the normwise condition number, the sensitivity of the relative condition number itself is studied, and the componentwise perturbation is also investigated.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.1-16
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• 2006

The classical perturbation theory is extended to the weighted Kronecker product linear systems $W(A{\bigotimes}B)W\chi=h$. Upper bounds are derived for the normwise condition number.