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Condition number for the Drazin inverse and the Drazin-inverse solution of singular linear system with their condition numbers. (English) Zbl 1077.15007
The condition number for the Drazin inverse and the Drazin-inverse solution of singular linear systems $$Ax=b$$ are investigated under the $$P$$-norm and a componentwise perturbation. The assumptions $$\text{Im}(E) \subseteq \text{Im}(A^k)$$ and $$\text{Im}(E^T) \subseteq \text{Im}(A^k)^T$$ on the perturbation $$E$$ are assumed, where $$\text{Im}(E)$$ denotes the range of $$E$$, $$E^T$$ is the transpose of $$E$$ and $$k$$ is the index of $$A$$.

##### MSC:
 15A12 Conditioning of matrices 15A09 Theory of matrix inversion and generalized inverses
##### Software:
DGMRES; mctoolbox
Full Text:
##### References:
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