周期广义耦合 Sylvester 方程的扰动分析
Perturbation analysis for the periodic generalized coupled Sylvester equation
AI总结：
本文研究周期广义耦合 Sylvester 方程的扰动分析，推导了其范数逆向误差，并给出范数和分量扰动界，进而得到范数和有效条件数，同时给出了混合和分量条件数，通过数值例子验证结果。
摘要：
本文研究周期广义耦合 Sylvester（PGCS）方程的扰动分析。首先获得了该方程的范数逆向误差。然后，我们给出了其范数和分量扰动界，从而导出了范数和有效条件数。此外，还给出了PGCS方程的混合和分量条件数。为了高可靠性估计这些条件数，应用了概率谱范数估计器和统计条件估计方法。所得结果通过数值例子加以说明。
英文摘要：
In this paper, we consider the perturbation analysis for the periodic generalized coupled Sylvester (PGCS) equation. The normwise backward error for this equation is first obtained. Then, we present its normwise and componentwise perturbation bounds, from which the normwise and effective condition numbers are derived. Moreover, the mixed and componentwise condition numbers for the PGCS equation are also given. To estimate these condition numbers with high reliability, the probabilistic spectral norm estimator and the statistical condition estimation method are applied. The obtained results are illustrated by numerical examples.
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