预处理矩阵及其构造方法

Preconditioned Matrix and Its Structure Methods

为了提高线性代数方程组迭代法的数值稳定性和收敛速度,采用适当的预处理方法是必要的,本文从预处理共轭梯度法(PCG)的预处理方法出发,介绍了一些常用的预处理方法和相应的预处理矩阵,并分析了它们的适用条件,给出了预处理矩阵的判别原则。为线性代数方程组迭代法的高效求解提供一些有益帮助。

For the sake of improving numerical stability and convergence of iterative methods for linear algebraic equations, appropriate preconditioned methods are necessary. Based on preconditioned methods of PCG, this paper introduces some common preconditioned methods and relevant preconditioned matrixes. After applied conditions of the methods are analyzed, some important principles for estimating preconditioned matrixes are presented. It is anticipant to provide some availability ways about effective iterative methods for linear algebraic equations.