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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
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References:
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