TITLE:
A New Preconditioner with Two Variable Relaxation Parameters for Saddle Point Linear Systems with Highly Singular(1,1) Blocks
AUTHORS:
Yuping Zeng, Chenliang Li
KEYWORDS:
Saddle Point Linear Systems, Block Triangular Preconditioner, Krylov Subspace Methods
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.1 No.4,
December
9,
2011
ABSTRACT: In this paper, we provide new preconditioner for saddle point linear systems with (1,1) blocks that have a high nullity. The preconditioner is block triangular diagonal with two variable relaxation paremeters and it is extension of results in [1] and [2]. Theoretical analysis shows that all eigenvalues of preconditioned matrix is strongly clustered. Finally, numerical tests confirm our analysis.