TY - JOUR
T1 - Improved PMHSS Iteration Methods for Complex Symmetric Linear Systems
AU - Liu , Kai
AU - Gu , Guiding
JO - Journal of Computational Mathematics
VL - 2
SP - 278
EP - 296
PY - 2018
DA - 2018/09
SN - 37
DO - http://doi.org/10.4208/jcm.1702-m2017-0007
UR - https://global-sci.org/intro/article_detail/jcm/12680.html
KW - Complex symmetric linear system, PMHSS.
AB - <p style="text-align: justify;">Based on the preconditioned modified Hermitian and skew-Hermitian splitting (PMHSS)
iteration method for the complex symmetric linear system, two improved iterative
methods, namely, the modified PMHSS (MPMHSS) method and the double modified
PMHSS (DMPMHSS) method, are proposed in this paper. The spectral radii of the
iteration matrices of two methods are given. We show that by choosing an appropriate
parameter, MPMHSS could speed up the convergence on PMHSS. The DMPMHSS
method is a four-step alternating iteration that is developed upon the two-step alternating
iteration of MPMHSS. We discuss the choice of the parameters and establish the convergence
of DMPMHSS. In particular, we give an analysis of the spectral radius of PMHSS
and DMPMHSS at the parameter free situation, and we show that DMPMHSS converges
faster than PMHSS in most cases. Our numerical experiments show these points.</p>