【作者】 孟国艳；

【导师】 王川龙；

【作者基本信息】 太原理工大学 ， 应用数学， 2003， 硕士

【摘要】 本文研究了解决大型稀疏对称正定线性方程组的一类预条件共轭梯度法。全文共分为四章。 第一章是对目前国内外研究现状的一个描述。 第二章提出了一种新的预条件共轭梯度法SAOR-AL-PCG。这种方法基于SAOR迭代法以及交错法，构造了预条件子M，然后利用共轭梯度法来求解预条件方程MAx=Mb。 第三章对这种预条件共轭梯度法进行了分析。推导出了它的条件数比原来系数矩阵的条件数要低。 第四章用实例证明了这种预条件共轭梯度法的收敛速度比古典的迭代法(如Jacobi，GS，SOR)和传统的CG以及SSOR-PCG要快一些。更多还原

【Abstract】 This paper is investigated a preconditioned conjugate gradient method in solving a linear algebraic system of large sparse symmetric and positive equations. There are four chapters in this paper altogether.In chapter 1, the overview is given about the study at present in the world.In chapter 2. I propose a new type of preconditioned conjugate gradient method, which is called SAOR-AL-PCG in brief. The preconditioner M is derived on the base of SAOR and the alternating method .Then we use conjugate gradient method to solve the preconditioned system MAx = Mb.In chapter 3, I analyze this algorithm and draw a conclusion its condition number is lower than CG algorithm’s.In chapter 4,some examples are given to illustrate that the convergence of SAOR-AL-PCG method is better than the classical iterative method(such as Jacobi. Gauss ?Seidel. SOR) and the traditional CG method as well as SSOR-PCG.更多还原