兰州大学机构库 >数学与统计学院
求解鞍点问题的广义含参不精确算法及其预处理
Alternative TitleOn generalized parameterized inexact methods and its preconditioning for saddle point problems
柴继斌
Thesis Advisor郑兵
2012-05-28
Degree Grantor兰州大学
Place of Conferral兰州
Degree Name硕士
Keyword非对称广义鞍点问题 Uzawa算法 含参不精确迭代算法 预处理 收敛性
Abstract鞍点问题在科学与工程的很多领域都有实际的应用,如混合有限元求解椭圆方程,流体力学,约束最优化,电磁学,最小二乘问题等.因此寻求快速有效的求解方法显得非常重要. 文章[43]中讨论了求解系数矩阵中(2,2)块为零的对称鞍点问题,提出了一类含参不精确迭代算法,本文将把它进行推广用以求解(2,1)块与(1,2)块不相等的大型稀疏广义非对称鞍点问题,文章讨论了算法在某些条件下的收敛性,并给出了预处理矩阵的特征值及其分布情况,而且在矩阵分裂中,通过选择不同的参数矩阵可以得到若干求解非对称鞍点问题的算法.最后的数值实验验证了在本文中新提的算法的有效性.
Other AbstractSaddle point problems arises in many scientific computations and engineering applications,such as mixed finite element methods for solving elliptic partial differential equations, constraint optimization,least squares problem,fluid dynamics,elasticity and so on.So it is of great interest to develop fast and efficient methods. In paper [43],a parameterized inexact inexact iterative methods for solving symmetric saddle point problems with the (2,2)-block being zero was considered. In this paper,we extend it to the large sparse nonsymmetric generalized saddle point problems case by allowing the (1,2)-block to be not equal to the (2,1)-block. We proved that the iteration method is convergent under certain conditions,the spectral radius and distribution of the preconditioned matrix ware discussed.With different of the parameter matrices in the matrix splitting,we get several algorithms for solving the nonsymmetric generalized saddle point problem. Numerical experiments are used to show that our methods are feasible.
URL查看原文
Language中文
Document Type学位论文
Identifierhttps://ir.lzu.edu.cn/handle/262010/224808
Collection数学与统计学院
Recommended Citation
GB/T 7714
柴继斌. 求解鞍点问题的广义含参不精确算法及其预处理[D]. 兰州. 兰州大学,2012.
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