矩阵多分裂迭代法的收敛条件  

CONVERGENCE CONDITIONS FOR MATRIX MULTISPLITTING ITERATIVE METHODS

作　　者：蔡放[1] 熊岳山[2] 王广礼[1] 骆志刚[1] 

机构地区：[1]国防科技大学理学院数学系 [2]国防科技大学计算机学院,长沙410073

出　　处：《计算数学》2007年第4期367-376,共10页Mathematica Numerica Sinica

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.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 the multisplitting sequence is weakly regular when the coefficient matrix is monotone and 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.

关 键 词：线性方程组 矩阵多分裂 异步迭代 收敛条件 

分 类 号：O241.6[理学—计算数学]