多种超高阶次缔合勒让德函数计算方法的比较

扩展高阶和超高阶重力场模型的构制与应用的数值稳定性取决于超高阶次缔合勒让德函数的计算方法。文中详细介绍了现有的多种缔合勒让德函数的递推计算方法:标准前向列推法、标准前向行推法、跨阶次递推法和Belikov列推法。从计算速度、计算精度和计算溢出问题3个角度分析比较了阶次高至2 160阶的各种方法的优劣。通过数值试验证明,Belikov列推法和跨阶次递推法是计算超高阶次缔合勒让德函数较优的方法,而其他几种方法不能用于超高阶次缔合勒让德函数的计算。文中结论为超高阶次球谐综合与球谐分析的数值计算提供了可靠的依据。

Comparison of Computing Methods of the Ultra-high Degree and Order

The numerical stability of the construction and application of the ultra-high degree and order the Earth's gravity models lies on the computing methods of the ultra-high degree and order fully normalized associated Legendre functions(ALFs).In this paper,a lot of computing methods of ALFs including standard forward column method,standard forward row method,recursive method between every other order and degree,and Belikov column method,are detailedly discussed.Advantages and disadvantages of these methods are analyzed and compared from three aspects: numerical efficiency,numerical precision and arithmetic overflow,when the degree and order are up to 2 160.The Belikov column method and recursive method between every other order and degree are proved to be excellent and others are not fit to compute the ultra-high degree and order ALFs by numerical tests.The conclusions are useful for selecting computing methods of ALFs in spherical harmonic synthesis and analysis.