Variants of the accelerated parameterized inexact Uzawa method for saddle-point problems

Abstract

In this paper, based on the SOR and SSOR splittings of the (1,1) part of saddle-point coefficient matrix, some variants of the accelerated parameterized inexact Uzawa (VAPIU) method are proposed for solving nonsingular and singular saddle-point problems. By choosing different parameter matrices, we derive some existing and new iterative methods. The corresponding convergence and semi-convergence of the VAPIU methods for solving nonsingular and singular saddle-point problems are studied in depth, respectively. The preconditioning strategies based on the VAPIU splittings of the coefficient matrices are presented. Numerical experiments are provided, which confirms that these new methods need less CPU times per iteration step comparing with some other methods for solving both nonsingular and singular saddle-point problems.