| A SHIFT-SPLITTING PRECONDITIONER FOR NON-HERMITIAN POSITIVE DEFINITE MATRICES |
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| 作者姓名： | Zhong-zhi Bai Jun-feng Yin Yang-feng Su |
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| 作者单位： | [1]LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China [2]Department of Mathematics, Fudan University, Shanghai 200433, China |
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| 基金项目： | Research supported by The China NNSF 0utstanding Young Scientist Foundation （No.10525102）, The National Natural Science Foundation （No.10471146）, and The National Basic Research Program （No.2005CB321702）, P.R. China. |
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| 摘 要： |
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| 关 键 词： | 非厄密共轭正矩阵 矩阵分裂 预处理 Krylov子空间法 |
| 收稿时间： | 2005-05-08 |
| 修稿时间： | 2005-05-082006-01-23 |
A SHIFT-SPLITTING PRECONDITIONER FOR NON-HERMITIAN POSITIVE DEFINITE MATRICES |
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| Zhong-zhi Bai Jun-feng Yin Yang-feng Su.A SHIFT-SPLITTING PRECONDITIONER FOR NON-HERMITIAN POSITIVE DEFINITE MATRICES[J].Journal of Computational Mathematics,2006,24(4):539-552. |
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| Authors: | Zhong-zhi;Bai;Jun-feng;Yin;Yang-feng;Su |
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| Abstract: | A shift splitting concept is introduced and, correspondingly, a shift-splitting iteration scheme and a shift-splitting preconditioner are presented, for solving the large sparse system of linear equations of which the coefficient matrix is an ill-conditioned non-Hermitian positive definite matrix. The convergence property of the shift-splitting iteration method and the eigenvalue distribution of the shift-splitting preconditioned matrix are discussed in depth, and the best possible choice of the shift is investigated in detail. Numerical computations show that the shift-splitting preconditioner can induce accurate, robust and effective preconditioned Krylov subspace iteration methods for solving the large sparse non-Hermitian positive definite systems of linear equations. |
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| Keywords: | Non-Hermitian positive definite matrix Matrix splitting Preconditioning Krylov subspace method Convergence |
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