解线性方程组的误差分析与方程组病态的判断

设ｘ为线性方程组Ａｘ＝ｂ的精确解向量，ｘ为近似解向量．令Ａｘ＝Ｂ，δｘ＝ｘ－ｘ，δｂ＝ｂ－ｂ，值和都可用来判断近似解向量ｘ的好坏。本文讨论在线性方程组状态不同的情况下，判断结果的差异．又为判断条件数的太大提供了两个不等式．同时从理论上解释了文献［２］中判断线性方程组病态的两种方法．

Error analysis of linear equations and criteria for ill-conditioned equation sets

Let x be the exact solution of linear equation Ax= band x be its approximate solution. Let, then both values and can be used to judge the accuracy of the approximate solution x. In this paper are discussed the differences in the results of the two methods under different condition numbers. Alos , two ways for estimating the condition numbers are given. Meantime,the two methods for judging ill-conditioned linear equations given in 2] are explanined theoretically.