中文摘要：

完全规格化缔合勒让德函数递推算法的适用性是衡量算法优劣的重要标志。从第一相对数值精度、第二相对数值精度和计算速度等方面对4种常用的递推算法——标准向前列递推算法、标准向前行递推算法、跨阶次递推算法和Belikov递推算法的适用性进行分析。结果表明,标准向前行递推算法适用范围最小;对于cosθ∈[-1,1],在1 900阶内,标准向前列递推算法、跨阶次递推算法和Belikov递推算法均适用,且第1种算法速度最快;在3 000阶内,跨阶次递推算法和Belikov递推算法适用,且后者更优。

英文摘要：

The applicability of the recursive algorithms of fully normalized associated Legendre functions（FNALFs）is an important indicator to evaluate their quality.We discuss four recursive algorithms of FNALFs including the standard forward column algorithm,the standard forward row algorithm,the recursive algorithm between every other order and degree,and the Belikov algorithm.The applicability of these algorithms are evaluated and compared from three aspects：the first relative numerical accuracy,the second relative numerical accuracy,and the computation speed and efficiency.We prove that the applicable intervals of standard forward row algorithm are the least.Whileθ∈[-1,1],the standard forward column algorithm,the recursive algorithm between every other order and degree,and the Belikov algorithm are applicable for degrees less than 1 900,the first algorithm is the fastest.Furthermore,the recursive algorithm between every other order and degree,and the Belikov algorithm are applicable for degrees less than 3 000,with the latter being the best.