A splitting method for complex symmetric indefinite linear system

摘要

In this paper, not requiring that the Hermitian part of the complex symmetric linear system must be Hermitian positive definite, a class of splitting methods is established by the modified positive/negative-stable splitting (PNS) of the coefficient matrix and is called the MPNS method. Theoretical analysis shows that the MPNS method is absolutely convergent under proper conditions. Some useful properties of the corresponding MPNS-preconditioned matrix are obtained. Numerical experiments are reported to illustrate the efficiency of both the MPNS method and the MPNS preconditioner.