Perturbation Analysis And Error Estimate For*-Sylvester Matrix Equations

*-Sylvester matrix equations are very important in numerical linear algebra. The ex-istence and algorithm for the solution had attracted many researchers in recent years. In this thesis, we adopt a componentwise perturbation analysis for*-Sylvester matrix equa-tion. We define normwise, mixed and componentwise condition numbers for*-Sylvester matrix equations. The corresponding explicit expressions are derived. For the backward error analysis, we define a componentwise backward error. A sharp and easily computable bound is derived for the componentwise backward error. Based on small condition esti-mation, we devise the algorithms to estimate condition numbers for*-Sylvester matrix equations. Numerical examples show that our algorithms can give reliable estimations. The proposed componentwise backward error coincides with the actual situation from numerical example’s evidences.