A modified SSOR-like preconditioner for non-Hermitian positive definite matrices

A modified SSOR-like (MSSOR-like) preconditioner is constructed for a non-Hermitian positive definite linear system with a dominant Hermitian part. The eigenvalue distribution of the MSSOR-like preconditioned matrix and the convergence property of the corresponding MSSOR-like iteration method are discussed in depth. Numerical experiments show that the MSSOR-like preconditioner can lead to a high-speed and effectively preconditioned GMRES, even when the dominant Hermitian part of the coefficient matrix is not so strong. (c) 2020 IMACS. Published by Elsevier B.V. All rights reserved.