Abstract: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. While θ∈[-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.
LEI Weiwei,ZHANG Hanwei,LI Kai. Applicability Analysis for the Common Recursive Algorithms of Fully Normalized Associated Legendre Function[J]. jgg, 2016, 36(5): 386-.