On block-diagonally preconditioned accelerated parameterized inexact Uzawa method for singular saddle point problems

Abstract

Recently, [Z.-Z. Bai, Z.-Q.Wang, On parameterized inexact Uzawa methods for generalized saddle point problems, Linear Algebra Appl. 428 (2008) 2900–2932] studied a class of parameterized inexact Uzawa (PIU) methods and proposed a generalized and modified accelerated parameterized inexact Uzawa (APIU) iteration method for solving nonsingular saddle point problems. In this paper, we further generalize this method to obtain the block-diagonally preconditioned accelerated parameterized inexact Uzawa (BDP–APIU) method for solving singular saddle point problems. Theoretical analysis shows that the semi-convergence of this new method can be guaranteed. In addition, the quasi-optimal parameters of the new method are discussed. Numerical example is given to show the feasibility and effectiveness of the new method for solving singular saddle point problems.