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Volume 37, Issue 1
Improved Relaxed Positive-Definite and Skew-Hermitian Splitting Preconditioners for Saddle Point Problems

Yang Cao, Zhiru Ren & Linquan Yao

DOI: 10.4208/jcm.1710-m2017-0065

J. Comp. Math., 37 (2019), pp. 95-111.

Published online: 2018-08

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  • Abstract

We establish a class of improved relaxed positive-definite and skew-Hermitian splitting (IRPSS) preconditioners for saddle point problems. These preconditioners are easier to be implemented than the relaxed positive-definite and skew-Hermitian splitting (RPSS) preconditioner at each step for solving the saddle point problem. We study spectral properties and the minimal polynomial of the IRPSS preconditioned saddle point matrix. A theoretical optimal IRPSS preconditioner is also obtained. Numerical results show that our proposed IRPSS preconditioners are superior to the existing ones in accelerating the convergence rate of the GMRES method for solving saddle point problems.

  • Keywords

Saddle point problems, Preconditioning, RPSS preconditioner, Eigenvalues, Krylov subspace method.

  • AMS Subject Headings

65F10, 65F50

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

caoyangnt@ntu.edu.cn (Yang Cao)

renzr@lsec.cc.ac.cn (Zhiru Ren)

lqyao@suda.edu.cn (Linquan Yao)

  • BibTex
  • RIS
  • TXT
@Article{JCM-37-95, author = {Cao , YangRen , Zhiru and Yao , Linquan}, title = {Improved Relaxed Positive-Definite and Skew-Hermitian Splitting Preconditioners for Saddle Point Problems}, journal = {Journal of Computational Mathematics}, year = {2018}, volume = {37}, number = {1}, pages = {95--111}, abstract = {

We establish a class of improved relaxed positive-definite and skew-Hermitian splitting (IRPSS) preconditioners for saddle point problems. These preconditioners are easier to be implemented than the relaxed positive-definite and skew-Hermitian splitting (RPSS) preconditioner at each step for solving the saddle point problem. We study spectral properties and the minimal polynomial of the IRPSS preconditioned saddle point matrix. A theoretical optimal IRPSS preconditioner is also obtained. Numerical results show that our proposed IRPSS preconditioners are superior to the existing ones in accelerating the convergence rate of the GMRES method for solving saddle point problems.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1710-m2017-0065}, url = {http://global-sci.org/intro/article_detail/jcm/12651.html} }
TY - JOUR T1 - Improved Relaxed Positive-Definite and Skew-Hermitian Splitting Preconditioners for Saddle Point Problems AU - Cao , Yang AU - Ren , Zhiru AU - Yao , Linquan JO - Journal of Computational Mathematics VL - 1 SP - 95 EP - 111 PY - 2018 DA - 2018/08 SN - 37 DO - http://doi.org/10.4208/jcm.1710-m2017-0065 UR - https://global-sci.org/intro/article_detail/jcm/12651.html KW - Saddle point problems, Preconditioning, RPSS preconditioner, Eigenvalues, Krylov subspace method. AB -

We establish a class of improved relaxed positive-definite and skew-Hermitian splitting (IRPSS) preconditioners for saddle point problems. These preconditioners are easier to be implemented than the relaxed positive-definite and skew-Hermitian splitting (RPSS) preconditioner at each step for solving the saddle point problem. We study spectral properties and the minimal polynomial of the IRPSS preconditioned saddle point matrix. A theoretical optimal IRPSS preconditioner is also obtained. Numerical results show that our proposed IRPSS preconditioners are superior to the existing ones in accelerating the convergence rate of the GMRES method for solving saddle point problems.

Cao , YangRen , Zhiru and Yao , Linquan. (2018). Improved Relaxed Positive-Definite and Skew-Hermitian Splitting Preconditioners for Saddle Point Problems. Journal of Computational Mathematics. 37 (1). 95-111. doi:10.4208/jcm.1710-m2017-0065
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