完全规格化缔合勒让德函数及其导数的递推算法与适用范围比较

Comparison of recursive algorithm and its applicable interval of fully normalized associated Legendre functions with their derivative

完全规格化缔合勒让德函数及其导数常用标准向前列递推算法和标准向前行递推算法进行计算。基于第一、第二相对数值精度标准对两种算法的适用范围进行分析比较,计算结果表明,标准向前列递推算法的适用范围大于标准向前行递推算法,说明前者优于后者;结果同时还表明,完全规格化缔合勒让德函数与其导数同一种算法的适用范围也相同,并指出了二者适用范围相同的原因。

The recursive algorithms including standard forward column algorithm and standard forward row algorithm are the common methods to calculate fully normalized associated Legendre functions and their derivative .In this paper ,the applicable interval of these recursive algorithms is determined based on the first and second numerical accuracy of the algorithm .The results indicate the interval of standard forward column algorithm is bigger than standard forward row algorithm ,so the former algorithm is better than the latter .It also indicates the applicable interval of the same algorithm of the fully normalized associated Legendre functions and their derivative are also the same ,and the reasons of that are explained .