改进的求解线性方程组的升阶法

A Correcting Order-increase Algorithm for Solving Linear Equation System

升阶法是一种比较新的求解线性方程组的直接方法,在形式上是迭代格式,相对于Gauss消去法计算量减少了近一半,但也存在着数值不稳定的现象,本文采取了一种修正的策略,比较好的解决了这一问题,对升阶法做了一定程度的改进,事实证明改进是积极有效的.

The order-increasing algorithm is a kind of direct method in nature to solve linear systems. However, it is iterative in style. The cost of it is only about half of that of the Gaussian elimination method. But there is also numerical instability. In this paper, we propose a correct tactics to improve the order-increasing algorithm and to some extent avoid that instability. It is proved that our improvement is positive and effective.