Inexact block SSOR-like preconditioners for non-Hermitian positive definite linear systems of strong Hermitian parts

摘要

In this work, a class of inexact block SSOR-like preconditioners are proposed for the non-Hermitian positive definite linear system whose coefficient matrix is of a blockwise form. The novel preconditioners are based on the SSOR-like iteration method proposed by Bai (Numer. Linear Algebra Appl. 23, 37-60, 2016), but each of the diagonal blocks in the SSOR-like method is replaced by an approximation matrix which is easier to deal with. The estimated bounds for eigenvalues of the new preconditioned matrix, as well as the convergence property about the corresponding iteration method, are discussed. Finally, numerical experiments arise from the discretization of two-dimensional fractional diffusion equation and two-dimensional linear integro-differential equation are presented to confirm the theoretical analyses and illustrate the efficiency of the new preconditioners.