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Mathematical Problems in Engineering
Volume 2016 (2016), Article ID 5087237, 18 pages
http://dx.doi.org/10.1155/2016/5087237
Research Article

Generalized ASOR and Modified ASOR Methods for Saddle Point Problems

Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an, Shaanxi 710072, China

Received 19 December 2015; Revised 15 March 2016; Accepted 27 March 2016

Academic Editor: Ruben Specogna

Copyright © 2016 Zhengge 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

Recently, the accelerated successive overrelaxation- (SOR-) like (ASOR) method was proposed for saddle point problems. In this paper, we establish a generalized accelerated SOR-like (GASOR) method and a modified accelerated SOR-like (MASOR) method, which are extension of the ASOR method, for solving both nonsingular and singular saddle point problems. The sufficient conditions of the convergence (semiconvergence) for solving nonsingular (singular) saddle point problems are derived. Finally, numerical examples are carried out, which show that the GASOR and MASOR methods have faster convergence rates than the SOR-like, generalized SOR (GSOR), modified SOR-like (MSOR-like), modified symmetric SOR (MSSOR), generalized symmetric SOR (GSSOR), generalized modified symmetric SOR (GMSSOR), and ASOR methods with optimal or experimentally found optimal parameters when the iteration parameters are suitably chosen.