The spectral properties of the preconditioned matrix for nonsymmetric saddle point problems

作者:

Highlights:

摘要

In this paper, on the basis of matrix splitting, two preconditioners are proposed and analyzed, for nonsymmetric saddle point problems. The spectral property of the preconditioned matrix is studied in detail. When the iteration parameter becomes small enough, the eigenvalues of the preconditioned matrices will gather into two clusters—one is near (0,0) and the other is near (2,0)—for the PPSS preconditioner no matter whether A is Hermitian or non-Hermitian and for the PHSS preconditioner when A is a Hermitian or real normal matrix. Numerical experiments are given, to illustrate the performances of the two preconditioners.

论文关键词:65F10,Preconditioner,Matrix splitting,Eigenvalue analysis,Nonsymmetric saddle point problems,Spectral

论文评审过程:Received 27 May 2009, Revised 27 April 2010, Available online 10 June 2010.

论文官网地址:https://doi.org/10.1016/j.cam.2010.06.001