A generalized SHSS preconditioner for generalized saddle point problem

Abstract

In this paper, based on the simplified Hermitian and skew-Hermitian (SHSS) preconditioner, a new preconditioner, called the generalized SHSS (GSHSS) preconditioner, is considered to solve the generalized saddle point problem. We prove that the GSHSS iteration method is convergent if the iteration parameters satisfy appropriate conditions. In addition, it is proved that all eigenvalues of the GSHSS preconditioned matrix are real and non-unit eigenvalues are located in a positive interval. Numerical experiment is provided to show the effectiveness of the GSHSS preconditioner.