倾角函数递推稳定性分析

摘要

Many kinds of recursion methods of inclination function had been brought out in history.However,several methods were found to be unstable in the high order.By the magnitude analysis of inclination functions in the direction of recursion,the stability of the recursion relation of inclination function can be estimated.For the commonly-used three-term recursion,only the Mk(l) recursion is stable,the others are unstable.But the stability of the multi-term recursion is more complex,it is necessary to make an in-depth analysis.%历史上曾经提出了较多的倾角函数递推算法,但有一些已经被证明在高阶是不稳定的.通过对递推方向上倾角函数的数量级分析,可以判断倾角函数递推的稳定性.对于常用的3项递推,只有Mk(l)递推是稳定的,其他递推均是不稳定的.但是对于多项递推比较复杂,还需深入分析.