| (I+Smax)预条件Gauss-Seidel迭代法进一步探索 |
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| 引用本文： | 庄伟芬,卢琳璋. (I+Smax)预条件Gauss-Seidel迭代法进一步探索[J]. 厦门大学学报(自然科学版), 2004, 43(Z1): 349-352 |
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| 作者姓名： | 庄伟芬 卢琳璋 |
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| 作者单位： | 厦门大学数学科学学院,福建,厦门,361005 |
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| 基金项目： | 国家自然科学基金(10271099)资助 |
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| 摘 要： | Kotakemori研究了不可约对角占优Z 阵的(I Smax)预条件Gauss Seidel迭代法,并证明在一定条件下,进行(I Smax)预处理比(I S)预处理收敛效果更好.本文将其收敛性定理推广到具有广泛应用背景的H 阵,并将这两类预条件Gauss Seidel迭代法相结合对不可约非奇M 阵进行两次适当的预处理,数值例子表明这样可以大大加快Gauss Seidel迭代法的收敛速度.
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| 关 键 词： | 预条件Gauss-Seidel迭代法 收敛速度 H矩阵 |
| 文章编号： | 0438-0479(2004)S-349-04 |
| 修稿时间： | 2004-01-05 |
Further Study on (I+Smax) Preconditioning Gauss-Seidel Iterative Method |
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| ZHUANG Wei-fen,LU Lin-zhang. Further Study on (I+Smax) Preconditioning Gauss-Seidel Iterative Method[J]. Journal of Xiamen University(Natural Science), 2004, 43(Z1): 349-352 |
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| Authors: | ZHUANG Wei-fen LU Lin-zhang |
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| Abstract: | Hisashiki Kotakemori had proposed a preconditioner (I S_(max)) for irreducibly diagonally dominant Z-matrix, which achieves better convergence rate than the classical Gauss-Seidel method and even better than Modified Gauss-Seidel method with preconditioner (I S) under certain circumstances. We extend his convergence theorem to the case of H-matrix, and apply the preconditioner (I S_(max)) to twice preconditioning for irreducible non-singular M-matrix, combining with another preconditioner (I S). Numerical examples had been given to confirm that the convergence rate had been improved on considerably. |
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| Keywords: | preconditioning Gauss-Seidel iterative method convergence rate H-matrix |
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