T. Z. Huang, G. H. Cheng and S. Q. Shen, “New Block Triangular Preconditioners for Saddle Point Linear Sys- tems with Highly Sigular (1,1) Blocks,” Compututer Phy- sics Communications, Vol. 180, No. 2, 2009, pp. 192-196.

has been cited by the following article:

• 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.