Block Triangular Preconditioner Based on Accelerated AOR Splitting Method for Generalized Saddle Point Problem

Abstract

Block triangular preconditioner based on accelerated AOR (AAOR) splitting method for the generalized saddle point problem is proposed. The iterative scheme of the AAOR splitting method, block triangular preconditioner and its convergence are researched. The eigenvalues distributions of its preconditioned matrix are discussed under make some special choices for parameter matrix Q. The resulting AAOR preconditioner is used to precondition Krylov subspace method such as the restarted generalized minimal residual (GMRES) method for solving the equivalent formulation of the generalized saddle point problem. The theoretical results and effectiveness of the block triangular preconditioner based on accelerated AAOR splitting method are supported by a numerical example.