| 对称半正定矩阵的二级多分裂 |
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| 引用本文： | 张华隆.对称半正定矩阵的二级多分裂[J].同济大学学报(自然科学版),2003,31(10):1232-1236. |
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| 作者姓名： | 张华隆 |
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| 作者单位： | 同济大学,应用数学系,上海,200092 |
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| 摘 要： | 考虑由二级多分裂迭代法求出大规模线性系统方程并行解的问题 .通过研究二级方法与多分裂方法两者之间的相互联系之后 ,借助于矩阵的对角补偿约化矩阵 ,较深入地讨论了对称半正定矩阵的二级多分裂方法 .首先分析一般矩阵的二级多分裂方法的特征与收敛性 ;然后给出对称半正定矩阵二级多分裂方法的构造过程 ,并在此结果的基础上证明了该二级多分裂迭代法在分裂是正则与弱正则的条件下对任意的初始向量都是收敛的
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| 关 键 词： | 对称半正定矩阵 二级多分裂 对角补偿约化矩阵 收敛性 |
| 文章编号： | 0253-374X(2003)10-1232-05 |
| 修稿时间： | 2002年10月8日 |
Two-stage Multisplitting of Symmetric Positive Semidefinite Matrices |
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| ZHANG Hua-long.Two-stage Multisplitting of Symmetric Positive Semidefinite Matrices[J].Journal of Tongji University(Natural Science),2003,31(10):1232-1236. |
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| Authors: | ZHANG Hua-long |
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| Abstract: | This paper attempts to get the parallel solution of a large consistent linear system of equations by two?-stage multisplitting iterative method.After having studied the relationship between the two?-stage method and the multisplitting method,two?-stage multisplitting of symmetric positive semidefinite matrices are studied thoroughly by employing matrices of diagonally compensated reduced matrices.Firstly,the features and convergence of two?-stage multisplitting method of common matrices is analyzed.Secondly,constructing process of two?-stage multisplitting symmetric positive semidefinite matrices is obtained.Based on the above result,two?-state multisplitting iterative method is proved convergent for any initial vector if splitting is regular and weak regular. |
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| Keywords: | symmetric positive semidefinite matrix two?-stage multisplitting diagonally compensated reduction matrix convergence |
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