Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 545470, 12 pages
Research Article

A Polynomial Preconditioner for the CMRH Algorithm

1School of Mathematical Sciences, Xiamen University, Xiamen 361005, China
2School of Mathematics and Computer Science, Guizhou Normal University, Guiyang 550001, China

Received 4 June 2010; Revised 21 December 2010; Accepted 24 January 2011

Academic Editor: P. Liatsis

Copyright © 2011 Jiangzhou Lai 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.


Many large and sparse linear systems can be solved efficiently by restarted GMRES and CMRH methods Sadok 1999. The CMRH(m) method is less expensive and requires slightly less storage than GMRES(m). But like GMRES, the restarted CMRH method may not converge. In order to remedy this defect, this paper presents a polynomial preconditioner for CMRH-based algorithm. Numerical experiments are given to show that the polynomial preconditioner is quite simple and easily constructed and the preconditioned CMRH(m) with the polynomial preconditioner has better performance than CMRH(m).