采用Belikov列推和跨阶次递推方法计算超高阶缔合勒让德函数

Calculating the ultra-high-order associated legendre functions by Belikov column method and recursive method between every other order and degree

超高阶球谐重力场模型的精确构制与快速计算取决于缔合勒让德函数的计算方法。在前人研究的基础上,文中对适合超高阶缔合勒让德函数计算的Belikov列推和跨阶次递推方法进行介绍,为验证精度,通过两种途径对计算结果进行检验,并比较其计算速度。结果表明,采用两种算法得到的每个勒让德函数的绝对精度均优于10-12,在低阶,跨阶次递推方法的计算用时大约是Belikov列推法的2倍,随着阶数的升高,跨阶次递推算法表现出明显的速度优势。

Precision construction and rapid calculation of ultra-high-order spherical harmonic gravity field model,depend on the calculation method of the associated legendre functions. On the basis of previous studies, the suitable Belikov column method and recursion method between every other order and degree for ultra-high-order legendre function are introduced. The accuracy of calculations verified results in two ways after are their calculation speeds compared. The result shows that： every associated legendre function calculated by this two algorithms is obtained with absolute accuracy better than 10-12. In low-order, the recursion method between every other order and degree takes time as twice as Belikov column method extrapolation. As the order increasing, the recursion method between every other order and degree shows a significant speed advantage.