关于共轭斜量法解线性代数方程组迭代次数的讨论

A DISCUSSION OF ITERATION NUMBERS IN SOLVING LINEAR EQUATION SYSTEMS BY CONJUGATEGRADIENT METHOD

本文给出了A正定对称时用共轭斜量法解线性代数方程组Ax=b时迭代次数的进一步估计。本文指出迭代次数与A的不同特征值的个数有关,还与初始向量x^((0))有关。给出了x^((0))的选取原则。

This paper gives further estimate of iterative numbers when the conjugate gradient method is used to solve systems of linear equations Ax = b where A is a positive definite symmetric matrices. In this paper the relation of the iterative numbers with distinct eigenvalues numbers is discussed and the influence of initial vactors x(0) for iterative numbers as presented. In this paper, the principle of choice x(0) is given.