从误差传播论数值计算的设计算法

在数值计算中每一步都可能产生误差,而一个问题的解决,往往要经过成千上万次运算,实际研究中不可能每步都加以分析。因此,要掌握运算次数的多少,运算过程是否符合规律,需要记录的中间结果的多少就必须找出比较简洁、误差比较小、花费时间比较少的计算方法。文章从控制误差的传播和积累的角度提出几种简单的算法,有助于计算结果的可靠性并防止误差危害现象的产生。

Discussion of How to Design the Algorithm of Numerical Methods due to the Error Propagation

It is always possible to produce errors at the each step in numerical calculations. Hundreds of thousand calculations may be needed to solve one problem and we cannot analyze every step. Therefore, it is necessary to find one numerical method which is easy to use, has low error margins, and is less time requiring in calculations, more reliable in regularity, and better capacity for the recording of temporary results. This article presents some easy numerical methods to control the propagation of errors, whi...