Table of Contents
ISRN Computational Mathematics
Volume 2013, Article ID 507817, 8 pages
http://dx.doi.org/10.1155/2013/507817
Research Article

New Preconditioners for Nonsymmetric Saddle Point Systems with Singular Block

Department of Mathematics, Zhejiang Wanli University, Ningbo, Zhejiang 315100, China

Received 27 April 2013; Accepted 28 July 2013

Academic Editors: P. Amodio, L. Hajdu, H. J. Ruskin, and K. Wang

Copyright © 2013 Qingbing Liu. 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 investigate the solution of large linear systems of saddle point type with singular block by preconditioned iterative methods and consider two parameterized block triangular preconditioners used with Krylov subspace methods which have the attractive property of improved eigenvalue clustering with increased ill-conditioning of the block of the saddle point matrix, including the choice of the parameter. Meanwhile, we analyze the spectral characteristics of two preconditioners and give the optimal parameter in practice. Numerical experiments that validate the analysis are presented.