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Convergence properties of preconditioned Hermitian and skew-Hermitian splitting methods for non-Hermitian positive semidefinite matrices |
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| Authors: | Zhong-Zhi Bai Gene H. Golub Chi-Kwong Li. |
| Affiliation: | Department of Mathematics, Fudan University, Shanghai 200433, People's Republic of China, and State Key Laboratory of Scientific/Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, P.O. Box 2719, Beijing 100080, People's Republic of China ; Scientific Computing and Computational Mathematics Program, Department of Computer Science, Stanford University, Stanford, California 94305-9025 ; Department of Mathematics, The College of William & Mary, P.O. Box 8795, Williamsburg, Virginia 23187-8795 |
| 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. |
| Keywords: | Non-Hermitian matrix positive semidefinite matrix Hermitian and skew-Hermitian splitting splitting iteration method convergence. |
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