本文選題：鞍點問題 + 增廣線性系統(tǒng)��； 參考：《華東師范大學》2015年碩士論文

【摘要】：增廣線性方程組來源于科學計算中的不同應(yīng)用,比如加權(quán)最小二乘,Navier-Stokes 方程的有限元離散,約束最優(yōu)化,平衡系統(tǒng)和鞍點問題。在解增廣系統(tǒng)的文章中,Golub, Wu and Yuan (2001)提出了幾個超松弛(SOR)類的算法。通過用兩個參數(shù)加速SOR類算法,我們提出了解增廣系統(tǒng)的加速SOR(ASOR)方法。本文包含四章。第一章討論了增廣系統(tǒng)的迭代法,主要展示經(jīng)典方法和修正的SOR方法。第二章我們回顧了現(xiàn)有的一些方法,也給出了SOR類方法和預(yù)處理共軛梯度法(PCG)的一般框架。在第三章,我們提出了增廣系統(tǒng)的新分裂的ASOR方法,并給出了參數(shù)α和ω,ASOR方法和矩陣Q-1BTA-1B的特征值之間的關(guān)系,以及在合適條件下ASOR方法的收斂性。第四章主要給出了數(shù)值例子和數(shù)值結(jié)果,展示了在合適的參數(shù)選擇下ASOR方法的有效性和優(yōu)越性。我們將ASOR方法與SOR類方法(Golub, Wu and Yuan,2001), GSOR方法(Bai, Parlett and Wang,2005)和GSSOR方法(Chao, Zhang and Lu,2014)進行了比較.
[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 偽 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).
【學位授予單位】：華東師范大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：O241.8

【相似文獻】

相關(guān)期刊論文 前1條

1 童調(diào)生;離散多延時系統(tǒng)的增廣系統(tǒng)[J];科學通報;1988年06期

相關(guān)會議論文 前1條

1 鄧自立;石瑩;;應(yīng)用Diophantine方程的最優(yōu)去卷[A];1997中國控制與決策學術(shù)年會論文集[C];1997年

相關(guān)碩士學位論文 前1條

1 Patrick Njue Njeru;加速的超松弛（ASOR）方法[D];華東師范大學;2015年

，

本文編號：2072977