ON HERMITIAN AND SKEW-HERMITIAN SPLITTING ITERATION METHODS FOR CONTINUOUS SYLVESTER EQUATIONS  

作　　者：Zhong-Zhi Bai 

机构地区：[1]LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

出　　处：《Journal of Computational Mathematics》2011年第2期185-198,共14页计算数学（英文）

摘　　要：We present a Hermitian and skew-Herrnitian splitting （HSS） iteration method for solving large sparse continuous Sylvester equations with non-Hermitian and positive definite/semi- definite matrices. The unconditional convergence of the HSS iteration method is proved and an upper bound on the convergence rate is derived. Moreover, to reduce the computing cost, we establish an inexact variant of the HSS iteration method and analyze its convergence property in detail. Numerical results show that the HSS iteration method and its inexact variant are efficient and robust solvers for this class of continuous Sylvester equations.We present a Hermitian and skew-Herrnitian splitting （HSS） iteration method for solving large sparse continuous Sylvester equations with non-Hermitian and positive definite/semi- definite matrices. The unconditional convergence of the HSS iteration method is proved and an upper bound on the convergence rate is derived. Moreover, to reduce the computing cost, we establish an inexact variant of the HSS iteration method and analyze its convergence property in detail. Numerical results show that the HSS iteration method and its inexact variant are efficient and robust solvers for this class of continuous Sylvester equations.

关 键 词：Continuous Sylvester equation HSS iteration method Inexact iteration Convergence. 

分 类 号：O242.23[理学—计算数学] TP273.2[理学—数学]