Volume 13, Issue 4
Regularized DPSS Preconditioners for Singular Saddle Point Problems

Yong Qian, Guofeng Zhang & Zhaozheng Liang

Numer. Math. Theor. Meth. Appl., 13 (2020), pp. 986-1006.

Published online: 2020-06

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  • Abstract

Recently, Cao proposed a regularized deteriorated positive and skew-Hermitian splitting (RDPSS) preconditioner for the non-Hermitian nonsingular saddle point problem. In this paper, we consider applying RDPSS preconditioner to solve the singular saddle point problem. Moreover, we propose a two-parameter accelerated variant of the RDPSS (ARDPSS) preconditioner to further improve its efficiency. Theoretical analysis proves that the RDPSS and ARDPSS methods are semi-convergent unconditionally. Some spectral properties of the corresponding preconditioned matrices are analyzed. Numerical experiments indicate that better performance can be achieved when applying the ARDPSS preconditioner to accelerate the GMRES method for solving the singular saddle point problem.

  • Keywords

Singular saddle point problem, DPSS preconditioner, preconditioning, semi-convergence.

  • AMS Subject Headings

65F10, 65F50

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-13-986, author = {Yong Qian , and Guofeng Zhang , and Zhaozheng Liang , }, title = {Regularized DPSS Preconditioners for Singular Saddle Point Problems}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2020}, volume = {13}, number = {4}, pages = {986--1006}, abstract = {

Recently, Cao proposed a regularized deteriorated positive and skew-Hermitian splitting (RDPSS) preconditioner for the non-Hermitian nonsingular saddle point problem. In this paper, we consider applying RDPSS preconditioner to solve the singular saddle point problem. Moreover, we propose a two-parameter accelerated variant of the RDPSS (ARDPSS) preconditioner to further improve its efficiency. Theoretical analysis proves that the RDPSS and ARDPSS methods are semi-convergent unconditionally. Some spectral properties of the corresponding preconditioned matrices are analyzed. Numerical experiments indicate that better performance can be achieved when applying the ARDPSS preconditioner to accelerate the GMRES method for solving the singular saddle point problem.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2019-0123}, url = {http://global-sci.org/intro/article_detail/nmtma/16963.html} }
TY - JOUR T1 - Regularized DPSS Preconditioners for Singular Saddle Point Problems AU - Yong Qian , AU - Guofeng Zhang , AU - Zhaozheng Liang , JO - Numerical Mathematics: Theory, Methods and Applications VL - 4 SP - 986 EP - 1006 PY - 2020 DA - 2020/06 SN - 13 DO - http://doi.org/10.4208/nmtma.OA-2019-0123 UR - https://global-sci.org/intro/article_detail/nmtma/16963.html KW - Singular saddle point problem, DPSS preconditioner, preconditioning, semi-convergence. AB -

Recently, Cao proposed a regularized deteriorated positive and skew-Hermitian splitting (RDPSS) preconditioner for the non-Hermitian nonsingular saddle point problem. In this paper, we consider applying RDPSS preconditioner to solve the singular saddle point problem. Moreover, we propose a two-parameter accelerated variant of the RDPSS (ARDPSS) preconditioner to further improve its efficiency. Theoretical analysis proves that the RDPSS and ARDPSS methods are semi-convergent unconditionally. Some spectral properties of the corresponding preconditioned matrices are analyzed. Numerical experiments indicate that better performance can be achieved when applying the ARDPSS preconditioner to accelerate the GMRES method for solving the singular saddle point problem.

Yong Qian, Guofeng Zhang & Zhaozheng Liang. (2020). Regularized DPSS Preconditioners for Singular Saddle Point Problems. Numerical Mathematics: Theory, Methods and Applications. 13 (4). 986-1006. doi:10.4208/nmtma.OA-2019-0123
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