加速的超松弛（ASOR）方法

发布时间：2018-06-27 06:23

本文选题：鞍点问题 + 增广线性系统　；参考：《华东师范大学》2015年硕士论文

【摘要】：增广线性方程组来源于科学计算中的不同应用,比如加权最小二乘,Navier-Stokes 方程的有限元离散,约束最优化,平衡系统和鞍点问题。在解增广系统的文章中,Golub, Wu and Yuan (2001)提出了几个超松弛(SOR)类的算法。通过用两个参数加速SOR类算法,我们提出了解增广系统的加速SOR(ASOR)方法。本文包含四章。第一章讨论了增广系统的迭代法,主要展示经典方法和修正的SOR方法。第二章我们回顾了现有的一些方法,也给出了SOR类方法和预处理共轭梯度法(PCG)的一般框架。在第三章,我们提出了增广系统的新分裂的ASOR方法,并给出了参数α和ω,ASOR方法和矩阵Q-1BTA-1B的特征值之间的关系,以及在合适条件下ASOR方法的收敛性。第四章主要给出了数值例子和数值结果,展示了在合适的参数选择下ASOR方法的有效性和优越性。我们将ASOR方法与SOR类方法(Golub, Wu and Yuan,2001), GSOR方法(Bai, Parlett and Wang,2005)和GSSOR方法(Chao, Zhang and Lu,2014)进行了比较.
[Abstract]:The augmented linear equations are derived from different applications in scientific computation, such as finite element discretization of weighted least squares Navier-Stokes equations, constrained optimization, equilibrium systems and saddle point problems. In this paper, Golub, Wu and Yuan (2001) proposed several algorithms of super relaxation (sor). By using two parameter accelerated sor class algorithms, we propose an accelerated sor (ASOR) method for solving augmented systems. This paper contains four chapters. In chapter 1, the iterative method of the augmented system is discussed, which mainly shows the classical method and the modified sor method. In chapter 2, we review some existing methods and give the general framework of the sor class method and the preconditioned conjugate gradient method (PCG). In the third chapter, we propose a new split ASOR method for augmented systems, and give the relationship between the parameter 伪 and 蠅 -Asaor method and the eigenvalues of the matrix Q-1BTA-1B, and the convergence of the ASOR method under suitable conditions. In the fourth chapter, numerical examples and numerical results are given to demonstrate the effectiveness and superiority of ASOR method under appropriate parameter selection. The ASOR method is compared with the sor method (Golub, Wu and Yuanl2001), the GSOR method (Bai, Parlett and Wang-2005) and the GSSOR method (Chao, Zhang and Luf2014).
【学位授予单位】：华东师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O241.8

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