求解鞍点系统的一类松弛预处理子
发布时间：2018-10-22 18:51
【摘要】：具有鞍点结构的大规模稀疏线性系统广泛来源于流体力学,约束优化控制,结构力学,线性规划,电路设计等诸多应用领域,其快速解法是近几年研究的热点之一.本文将正则化的思想运用到求解非对称鞍点系统的SIMPLE-like预处理子上[Z.-Z.Liang,G.-F.Zhang,J.Comput.Appl.Math.,302(2016)211-223],得到一个更为有效的预处理子,进一步将这个新预处理子推广到更一般的鞍点问题.我们对相应预处理矩阵的特征性质进行了详细地分析,对预处理矩阵的最小多项式的次数给出了相关结论.最后通过一些数值试验来说明所提出的新预处理子的有效性和可行性.
[Abstract]:Large-scale sparse linear systems with saddle point structures are widely derived from fluid mechanics, constrained optimal control, structural mechanics, linear programming, circuit design and so on. In this paper, the idea of regularization is applied to the SIMPLE-like preprocessor for solving asymmetrical saddle point systems [Z.-Z.Liangang G.-F.Zhang-J.Comput.appl.Math.Y302 (2016) 211-223], and a more effective preprocessor is obtained, which is further extended to a more general saddle point problem. The characteristic properties of the corresponding preprocessing matrix are analyzed in detail, and the relevant conclusions are given for the degree of the minimum polynomial of the preprocessing matrix. Finally, the validity and feasibility of the proposed new preprocessor are demonstrated by some numerical experiments.
【学位授予单位】：兰州大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O241.6
[Abstract]:Large-scale sparse linear systems with saddle point structures are widely derived from fluid mechanics, constrained optimal control, structural mechanics, linear programming, circuit design and so on. In this paper, the idea of regularization is applied to the SIMPLE-like preprocessor for solving asymmetrical saddle point systems [Z.-Z.Liangang G.-F.Zhang-J.Comput.appl.Math.Y302 (2016) 211-223], and a more effective preprocessor is obtained, which is further extended to a more general saddle point problem. The characteristic properties of the corresponding preprocessing matrix are analyzed in detail, and the relevant conclusions are given for the degree of the minimum polynomial of the preprocessing matrix. Finally, the validity and feasibility of the proposed new preprocessor are demonstrated by some numerical experiments.
【学位授予单位】：兰州大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O241.6
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