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On the condition mumbers for \(*\)-Sylvester matrix equation. (Chinese. English summary) Zbl 1349.65152

Summary: The condition number is a measurement for the sensitivity of solution to the perturbation in the data of a computational problem. It plays an important role in the perturbation analysis. In this paper, we deal with the condition numbers for the \(\ast\)-Sylvester equation \(AX+B^\ast X^\ast =C\), \(A\), \(B\), \(X\in\mathbb C^{n\times n}\). The explicit expressions of the mixed condition numbers, componentwise condition numbers, effective condition numbers and their upper bounds are derived respectively. Numerical examples illustrate the sharpness of our perturbation bounds.

MSC:

65F35 Numerical computation of matrix norms, conditioning, scaling
15A24 Matrix equations and identities
15A12 Conditioning of matrices
65F30 Other matrix algorithms (MSC2010)
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