| 预优矩阵及其构造技术 |
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| 引用本文： | 范啸涛,季光明. 预优矩阵及其构造技术[J]. 成都理工大学学报(自然科学版), 2003, 30(4): 432-435 |
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| 作者姓名： | 范啸涛 季光明 |
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| 作者单位： | 成都理工大学信息管理学院,成都,610059;成都理工大学信息管理学院,成都,610059 |
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| 摘 要： | 为达到预处理共轭梯度法(PCG)提高收敛速度,克服数值不稳定性目的,给出了构造预优矩阵的条件,并构造了三个典型的预优矩阵。它们是不完全Cholesky因子预优矩阵,对角预优矩阵和利用SSOR法导出的预优矩阵,且在PCG中是应用效果很好的预优矩阵。
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| 关 键 词： | 条件数 预处理共轭梯度法 不完全Cholesky分解 对称逐次超松弛迭代法 |
| 文章编号： | 1671-9727(2003)04-0432-04 |
| 修稿时间： | 2002-09-26 |
PRECONDITIONED MATRIX AND ITS STRUCTURE TECHNIQUE |
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| FAN Xiao tao,JI Guang ming. PRECONDITIONED MATRIX AND ITS STRUCTURE TECHNIQUE[J]. Journal of Chengdu University of Technology: Sci & Technol Ed, 2003, 30(4): 432-435 |
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| Authors: | FAN Xiao tao JI Guang ming |
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| Abstract: | In order to make the preconditioned conjugate gradient method(PCG) increase the convergence speed and overcome the number unstability, this paper gives the conditions to structure the preconditioned matrix and structure the three typical preconditioned matrixes. They are the preconditioned matrix with the incompletely Cholesky factor, the diagonal preconditioned matrix, and the preconditioned matrix induced by SSOR. They are effective preconditioned matrixs in PCG. |
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| Keywords: | condition number preconditioned conjugate gradient method incomplete Cholesky decomposition symmetric successive over relaxation iterative method |
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