TY - JOUR
T1 - On Hermitian and Skew-Hermitian Splitting Iteration Methods for Continuous Sylvester Equations
AU - Zhongzhi Bai
JO - Journal of Computational Mathematics
VL - 2
SP - 185
EP - 198
PY - 2011
DA - 2011/04
SN - 29
DO - http://doi.org/10.4208/jcm.1009-m3152
UR - https://global-sci.org/intro/article_detail/jcm/8472.html
KW - Continuous Sylvester equation, HSS iteration method, Inexact iteration, Convergence.
AB - <p style="text-align: justify;">We present a Hermitian and skew-Hermitian 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.</p>