An efficient variant of HSS preconditioner for generalized saddle point problems. Issue 4 (14th March 2018)

• Record Type: Journal Article
• Authors: Zhang, Ju‐Li
• Other Names: Bai Zhong‐Zhi guestEditor.; Neytcheva Maya G. guestEditor.; Reichel Lothar guestEditor.
• Is Part Of: Numerical linear algebra with applications. Volume 25:Issue 4(2018)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2018-03-14
• Subjects: generalized saddle point problem -- HSS preconditioner -- relaxation preconditioning technique -- spectral analysis; Algebras, Linear -- Periodicals; 512.5
• DOI: 10.1002/nla.2166
• Languages: English
• ISSNs: 1070-5325

Abstract

Summary: We present an efficient variant of the Hermitian and skew‐Hermitian splitting (HSS) preconditioner for generalized saddle point problems. By switching the positions of the two splitting matrices in the HSS preconditioner, together with some modifications combined with the relaxation preconditioning technique, we show that the new preconditioner is much closer to the coefficient matrix and easier to be implemented. Theoretical analyses show that the corresponding iteration method converges to the unique solution of the generalized saddle point problem under certain conditions. The spectral properties, including bounds on the eigenvalues and condition numbers of the eigenvectors, for the preconditioned matrix, are also discussed. Finally, numerical experiments are presented to illustrate the effectiveness of the new preconditioner.