# American Institute of Mathematical Sciences

2012, 2(4): 823-838. doi: 10.3934/naco.2012.2.823

## A new Bramble-Pasciak-like preconditioner for saddle point problems

 1 Nanhai College, South China Normal University, Foshan 528225, China 2 School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, China

Received  December 2011 Revised  October 2012 Published  November 2012

A new Bramble-Pasciak-like preconditioner with parameter is proposed for solving a linear system in the saddle point form. The system can be reformulated as a symmetric positive definite system with respect to some inner product and thus can be solved by the Bramble-Pasciak conjugate gradient (BPCG) method. Based on the spectral condition number of the associated system, the quasi-optimal parameters can be obtained to improve the convergence rate of the BPCG method. Numerical experiments on the Stokes problem are given to illustrate our theoretical results.
Citation: Xiao-Fei Peng, Wen Li. A new Bramble-Pasciak-like preconditioner for saddle point problems. Numerical Algebra, Control & Optimization, 2012, 2 (4) : 823-838. doi: 10.3934/naco.2012.2.823
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