Convergence Analysis of Modified Iterative Methods to Solve Linear Systems

Abstract

In the past years, a growing interest to solve linear systems with modified iterative methods has been shown by researchers. Recently, Dehghan and Hajarian (J Vib Control, doi: 10.1177/10775463124 , 2012)based on preconditioned methods, introduced modified accelerated overrelaxation methods for solving linear systems. These authors stated that the best property of the mentioned methods is that they can be used under mild conditions than the Milaszewicz’s (Linear Algebra Appl 93:161–170, 1987) preconditioner. In this paper, we show that the Milaszewicz’s preconditioner is applicable under mild conditions and also, under these conditions, Milaszewicz’s preconditioner is superior to the Dehghan and Hajarian’s preconditioner. Numerical examples are also given to illustrate our results.