Several preconditioners are proposed for improving the convergence rate of the iterative method derived from splitting. In this paper, the comparison theorem of preconditioned iterative method for regular splitting is proved. And the convergence and comparison theorem for any preconditioner are indicated. This comparison theorem indicates the possibility of finding new preconditioner and splitt...

In this paper, we study the iterative algorithms for saddle point problems(SPP). Bai, Golub and Pan recently studied a class of preconditioned Hermitian and skew-Hermitian splitting methods(PHSS). By further accelerating it with another parameters, using the Hermitian/skew-Hermitian splitting iteration technique we present the generalized preconditioned Hermitian and skew-Hermitian splitting me...

A qualitative analysis of one-step iterative methods is presented with special regard to the connection between concavity preservation and time-monotonicity. We also analyze the relation of one-step iterative methods to matrix splitting methods. c © 2007 Elsevier Ltd. All rights reserved.

For large-scale sparse saddle point problems, Peng and Li [12] have recently proposed a new alternating-direction iterative method for solving nonsingular saddle point problems, which is more competitive (in terms of iteration steps and CPU time) than some classical iterative methods such as Uzawa-type and HSS (Hermitian skew splitting) methods. In this paper, we further study this method when ...

in this work, a new iterative method is proposed for obtaining the approximate solution of a class of hammerstein type integral equations system. the main structure of this method is based on the richardson iterative method for solving an algebraic linear system of equations. some conditions for existence and unique solution of this type equations are imposed. convergence analysis and error bou...

In this article we consider iterative operator-splitting methods for nonlinear differential equations with respect to their eigenvalues. The main feature of the proposed idea is the fixed-point iterative scheme that linearizes our underlying equations. Based on the approximated eigenvalues of such linearized systems we choose the order of the the operators for our iterative splitting scheme. Th...

In this paper we describe a different operator-splitting method for decoupling complex equations with multi-dimensional and multiphysical processes for applications for porous media and phase-transitions. We introduce different operator-splitting methods with respect to their usability and applicability in computer codes. The error-analysis for the iterative operator-splitting methods is discus...