预条件共轭斜量法及其在求解边值问题中的应用

PRECONDITIONED CONJUGATE GRADIENT METHOD AND ITS APPLICATION TO SOLVING BOUNDARY VALUE PROBLEM

在论证共轭斜量法误差估计式的基础上 ,为提高敛速 ,对系数矩阵进行预处理 ,提供了减少等价问题条件数的方法 ,完美地建立了预条件共轭斜量法的实用算法。最后 ,以泊松方程边值问题为例 ,通过数值实验说明了该方法的有效性。

Based on proving the error estimate formula of conjugate gradient method(CG), this paper makes a pretreatment of coefficient matrix in order to improve convergence speed. This disposal provides the method of reducing the condition number of equivalence problem. So it perfectly establishes the practical algorithm of preconditioned conjugate gradient method(PCG). At last, taking the boundary value problem of Poisson equation as an example, this paper illuminates the validity of this method through numerical experiment.