New Block Triangular Preconditioners for Saddle Point Linear Systems with Highly Singular (1,1) Blocks | Zendy

TingZhu Huang | Zendy; Guanghui Cheng | Zendy; Liang Li | Zendy

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New Block Triangular Preconditioners for Saddle Point Linear Systems with Highly Singular (1,1) Blocks

Author(s) -

TingZhu Huang,

Guanghui Cheng,

Liang Li

Publication year - 2009

Publication title -

mathematical problems in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.262

H-Index - 62

eISSN - 1026-7077

pISSN - 1024-123X

DOI - 10.1155/2009/468965

Subject(s) - saddle point , eigenvalues and eigenvectors , mathematics , block (permutation group theory) , saddle , singular value , point (geometry) , linear system , mathematical analysis , combinatorics , mathematical optimization , geometry , physics , quantum mechanics

We establish two types of block triangular preconditioners applied to the linear saddle point problems with the singular (1,1) block. These preconditioners are based on the results presented in the paper of Rees and Greif (2007). We study the spectral characteristics of the preconditioners and show that all eigenvalues of the preconditioned matrices are strongly clustered. The choice of the parameter is involved. Furthermore, we give the optimal parameter inpractical. Finally, numerical experiments are also reported for illustrating the efficiency of the presented preconditioners

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