Perturbation analysis for the periodic generalized coupled Sylvester equation

Abstract

ABSTRACTIn this paper, we consider the perturbation analysis for the periodic generalized coupled Sylvester (PGCS) equation. The normwise backward error for this equation is first investigated. Then, we present its normwise and componentwise perturbation bounds using the fixed-point theorem, 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 and two algorithms are devised. The obtained results are illustrated by numerical experiments.