求解特定鞍点问题的改进SOR-Like方法
发布时间：2018-11-04 09:03
【摘要】：鞍点问题广泛出现在众多的工程研究领域,如流体力学、电磁学、最优化问题、最小二乘问题、椭圆偏微分方程问题等.以SOR类方法为基础,结合HS分裂思想,将经典鞍点问题的求解方法推广到特殊鞍点问题的求解上.给出一种具有新型分裂迭代格式的MSOR-Like方法,用以求解一类含有非对称块的鞍点系统,给出了相应的收敛性分析以及最优松弛参数选取方法.数值算例验证了对于不同的预优矩阵,MSORLike方法只有收敛速度的分别,没有收敛性能的影响,且在相同计算精度下,该方法解决特殊鞍点问题的迭代效果优于常规方法解决经典鞍点问题.
[Abstract]:Saddle point problems are widely used in many engineering fields, such as hydrodynamics, electromagnetism, optimization problems, least squares problems, elliptic partial differential equations and so on. Based on the SOR class method and the HS splitting idea, the classical saddle point problem solution method is extended to the special saddle point problem solution. A new split iterative MSOR-Like method is presented to solve a class of saddle point systems with asymmetric blocks. The corresponding convergence analysis and optimal relaxation parameter selection method are given. Numerical examples show that for different preoptimal matrices, the MSORLike method has only the difference of convergence rate and has no effect on the convergence performance, and under the same calculation precision, The iterative effect of this method for solving special saddle point problem is better than that of conventional method.
【作者单位】： 东北大学理学院;
【基金】：国家自然科学基金资助项目(11371081)
【分类号】：O241.6
[Abstract]:Saddle point problems are widely used in many engineering fields, such as hydrodynamics, electromagnetism, optimization problems, least squares problems, elliptic partial differential equations and so on. Based on the SOR class method and the HS splitting idea, the classical saddle point problem solution method is extended to the special saddle point problem solution. A new split iterative MSOR-Like method is presented to solve a class of saddle point systems with asymmetric blocks. The corresponding convergence analysis and optimal relaxation parameter selection method are given. Numerical examples show that for different preoptimal matrices, the MSORLike method has only the difference of convergence rate and has no effect on the convergence performance, and under the same calculation precision, The iterative effect of this method for solving special saddle point problem is better than that of conventional method.
【作者单位】： 东北大学理学院;
【基金】：国家自然科学基金资助项目(11371081)
【分类号】：O241.6
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