1. Perturbation analysis for the periodic generalized coupled Sylvester equation
- Author
-
Shaoxin Wang, Chan Zheng, and Hanyu Li
- Subjects
0209 industrial biotechnology ,Applied Mathematics ,Mathematical analysis ,Probabilistic logic ,Matrix norm ,Fixed-point theorem ,Perturbation (astronomy) ,Estimator ,Numerical Analysis (math.NA) ,010103 numerical & computational mathematics ,02 engineering and technology ,01 natural sciences ,Computer Science Applications ,020901 industrial engineering & automation ,Computational Theory and Mathematics ,FOS: Mathematics ,Mathematics - Numerical Analysis ,0101 mathematics ,Sylvester equation ,Condition number ,65F35, 15A12, 15A24 ,Mathematics - Abstract
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., 15 pages, 1 figure
- Published
- 2017