A generalization of the inexact parameterized Uzawa methods for saddle point problems

Abstract

For large sparse saddle point problems, Bai and Wang recently studied a class of parameterized inexact Uzawa methods (see Z.-Z. Bai, Z.-Q. Wang, On paramaterized inexact Uzawa methods for generalized saddle point problems, Linear Algebra Appl. 428 (2008) 2900–2932). In this paper, we generalize these methods and propose a class of generalized inexact parameterized iterative schemes for solving the saddle point problems. We derive conditions for guaranteeing the convergence of these iterative methods. With different choices of the parameter matrices, the generalized iterative methods lead to a series of existing and new iterative methods including the classical Uzawa method, the inexact Uzawa method, the GSOR method and the GIAOR method.