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| 矩阵多分裂迭代法的收敛条件 | |
| 引用本文： | 蔡放,熊岳山,王广礼,骆志刚.矩阵多分裂迭代法的收敛条件[J].计算数学,2007,29(4):367-376. |
| 作者姓名： | 蔡放 熊岳山 王广礼 骆志刚 |
| 作者单位： | 1. 国防科技大学理学院数学系,长沙,410073;长沙大学数学与信息科学系,长沙,410003 2. 国防科技大学计算机学院,长沙,410073 3. 国防科技大学理学院数学系,长沙,410073 |
| 摘 要： | 本文给出了求解非奇异线性方程组的矩阵多分裂并行迭代法的一些新的收敛结果.当系数矩阵单调和多分裂序列为弱正则分裂时,得到了几个与已有的收敛准则等价的条件,并且证明了异步迭代法在较弱条件下的收敛性.对于同步迭代,给出了与异步迭代不同且较为宽松的收敛条件. |
| 关 键 词： | 线性方程组 矩阵多分裂 异步迭代 收敛条件 |
| 修稿时间： | 2005-10-28 |
CONVERGENCE CONDITIONS FOR MATRIX MULTISPLITTING ITERATIVE METHODS |
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| Cai Fang,Xiong Yueshan,Wang Liguang,Luo Zhigang.CONVERGENCE CONDITIONS FOR MATRIX MULTISPLITTING ITERATIVE METHODS[J].Mathematica Numerica Sinica,2007,29(4):367-376. | |
| Authors: | Cai Fang Xiong Yueshan Wang Liguang Luo Zhigang |
| Affiliation: | 1. Department of Mathematics, School of Science, National University of Defense Technology, Changsha 410073, China;2. Department of Mathematics and Information Science, ChangSha University, Changsha 410003, China;3. School of Computer, National University of Defense Technology, Changsha 410073, China |
| Abstract: | We present some new convergence results with regard to parallel matrix multisplitting iterations for the solution of linear systems of equations.Several conditions equivalent to the known convergence criteria are obtained when the coefficient matrix is monotone and the multisplitting sequence is weakly regular.Moreover,the convergence of asynchronous iterations is shown under a weaker condition.We also give a convergence condition for the synchronous iterations,which is different from and weaker than that of the asynchronous iterations. |
| Keywords: | Linear systems of equations Matrix multisplittings Asynchronous iterative methods Convergence conditions |
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