Modified block product preconditioner for a class of complex symmetric linear systems

Abstract

This paper introduces a modified block product preconditioner for a class of complex symmetric linear systems which is constructed by the equivalent real block two-by-two structure of the coefficient matrix. We discuss the convergence of the associated iterative method and determine the optimal choice of the iteration parameter. Furthermore, some algebraic properties of the preconditioned matrix are studied. The proposed preconditioner can be applied to accelerate the convergence of the Krylov subspace methods like GMRES. Finally, the numerical experiments are used to show that the new preconditioner can be effective for solving the linear system of equations arising from the solution of the complex symmetric indefinite linear systems.