Convergence properties of preconditioned Hermitian and skew-Hermitian splitting methods for non-Hermitian positive semidefinite matrices

Bai, Zhong-Zhi; Golub, Gene; Li, Chi-Kwong

doi:10.1090/S0025-5718-06-01892-8

Convergence properties of preconditioned Hermitian and skew-Hermitian splitting methods for non-Hermitian positive semidefinite matrices

Authors: Zhong-Zhi Bai, Gene H. Golub and Chi-Kwong Li
Journal: Math. Comp. 76 (2007), 287-298
MSC (2000): Primary 65F10, 65F50
DOI: https://doi.org/10.1090/S0025-5718-06-01892-8
Published electronically: August 31, 2006
MathSciNet review: 2261022
Full-text PDF Free Access

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Abstract: For the non-Hermitian and positive semidefinite systems of linear equations, we derive necessary and sufficient conditions for guaranteeing the unconditional convergence of the preconditioned Hermitian and skew-Hermitian splitting iteration methods. We then apply these results to block tridiagonal linear systems in order to obtain convergence conditions for the corresponding block variants of the preconditioned Hermitian and skew-Hermitian splitting iteration methods.

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