Mathematical Problems in Engineering
Volume 2009 (2009), Article ID 794589, 9 pages
Research Article

A Modification of Minimal Residual Iterative Method to Solve Linear Systems

1School of Mathematics and Computer Science, Fuyang Normal College, Fuyang Anhui 236032, China
2Department of Mathematics, East China Normal University, Shanghai 200062, China

Received 25 November 2008; Revised 16 February 2009; Accepted 4 March 2009

Academic Editor: Alois Steindl

Copyright © 2009 Xingping Sheng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We give a modification of minimal residual iteration (MR), which is 1V-DSMR to solve the linear system Ax=b. By analyzing, we find the modifiable iteration to be a projection technique; moreover, the modification of which gives a better (at least the same) reduction of the residual error than MR. In the end, a numerical example is given to demonstrate the reduction of the residual error between the 1V-DSMR and MR.