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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2016, Volume 19, Number 3, Pages 267–279
DOI: https://doi.org/10.15372/SJNM20160303 (Mi sjvm617) 		 
Preconditioning of GMRES by the skew-Hermitian iterations

L. A. Krukier, T. S. Martynova

Institute of Mathematics, Mechanics and Computer Sciences, Southern Federal University, 200/1, bld. 2, Stachki pr., Rostov-on-Don, 344090, Russia
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DOI: https://doi.org/10.15372/SJNM20160303
Abstract: A class of preconditioners for solving non-Hermitian positive definite systems of linear algebraic equations is proposed and investigated. It is based on the Hermitian and skew-Hermitian splitting of the initial matrix. The generalization for saddle point systems which have semidefinite or singular $(1,1)$ blocks is given. Our approach is based on an augmented Lagrangian formulation. It is shown that such preconditioners are effective for the iterative solution of systems of linear algebraic equations by the GMRES.
Key words: Hermitian and skew-Hermitian splitting, iterative methods, preconditioning, Krylov subspace method, saddle point linear system.
Funding agency Grant number
Russian Foundation for Basic Research 15-01-00441-а
15-51-53066 ГФЕН-а
Ministry of Education and Science of the Russian Federation 1420
Received: 23.10.2015
Revised: 14.12.2015
English version:
Numerical Analysis and Applications, 2016, Volume 9, Issue 3, Pages 207–217
DOI: https://doi.org/10.1134/S1995423916030034
Bibliographic databases:
Document Type: Article
UDC: 519.6
Language: Russian
Citation: L. A. Krukier, T. S. Martynova, “Preconditioning of GMRES by the skew-Hermitian iterations”, Sib. Zh. Vychisl. Mat., 19:3 (2016), 267–279; Num. Anal. Appl., 9:3 (2016), 207–217
Citation in format AMSBIB
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