Geng, Xue; Wang, Weiguo On the condition mumbers for \(*\)-Sylvester matrix equation. (Chinese. English summary) Zbl 1349.65152 Period. Ocean Univ. China 45, No. 6, 132-138 (2015). 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) Keywords:\(\ast\)-Sylvester equation; mixed condition numbers; componentwise condition numbers; effective condition numbers; numerical examples; perturbation bounds PDFBibTeX XMLCite \textit{X. Geng} and \textit{W. Wang}, Period. Ocean Univ. China 45, No. 6, 132--138 (2015; Zbl 1349.65152) Full Text: DOI