SOR-like Methods With Optimization Model for Augmented Linear Systems
SOR-like Methods With Optimization Model for Augmented Linear Systems
复制标题
增强线性系统优化模型的类 SOR 方法
DOI：
10.4208/eajam.010916.261116a
复制
发表时间：
2017-02-01
影响因子：
1.2
通讯作者：
Meng, Guo-Yan
中科院分区：
文献类型：
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作者：
Wen, Rui-Ping;Li, Su-Dan;Meng, Guo-Yan
自Golub、Wu和Yuan十五年前发表杰出工作（BIT 41（2001）71-85）以来，人们对求解增广线性方程组的类SOR方法进行了大量研究。在类SOR方法的基础上，利用最优化技术建立了求解大型稀疏增广线性方程组的一类加速类SOR方法，该方法通过优化模型来寻找最优松弛参数ω.在适当的限制条件下，我们证明了新方法的收敛性理论。数值算例表明了这些方法的有效性。
There has been a lot of study on the SOR-like methods for solving the augmented system of linear equations since the outstanding work of Golub, Wu and Yuan (BIT 41(2001) 71-85) was presented fifteen years ago. Based on the SOR-like methods, we establish a class of accelerated SOR-like methods for large sparse augmented linear systems by making use of optimization technique, which will find the optimal relaxation parameter omega by optimization models. We demonstrate the convergence theory of the new methods under suitable restrictions. The numerical examples show these methods are effective.