Mathematical Problems in Engineering
Volume 2009 (2009), Article ID 468965, 13 pages
doi:10.1155/2009/468965
Research Article

New Block Triangular Preconditioners for Saddle Point Linear Systems with Highly Singular (1,1) Blocks

TingZhu Huang, GuangHui Cheng, and Liang Li

School of Applied Mathematics/Institue of Computational Science, University of Electronic Science and Technology of China, Chengdu, Sichuan 610054, China

Received 10 December 2008; Revised 29 March 2009; Accepted 6 August 2009

Academic Editor: Victoria Vampa

Copyright © 2009 TingZhu Huang 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.

Abstract

We establish two types of block triangular preconditioners applied to the linear saddle point problems with the singular (1,1) block. These preconditioners are based on the results presented in the paper of Rees and Greif (2007). We study the spectral characteristics of the preconditioners and show that all eigenvalues of the preconditioned matrices are strongly clustered. The choice of the parameter is involved. Furthermore, we give the optimal parameter in practical. Finally, numerical experiments are also reported for illustrating the efficiency of the presented preconditioners.