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- W831722154 abstract "Spherical harmonic expansions form partial sums of fully normalised associated Legendre functions [ALFs], which, for ultra-high degree and order (eg.~2700), range over thousands of orders of magnitude towards the poles. This causes existing recursion techniques for computing values of individual ALFs and their derivatives to fail. Alternatively, high degree synthesis is possible using Clenshaw’s (1955) method. Straightforward numerical principles govern the stability of this technique. Suprisingly, existing algorithms for computing ALFs and their first and second derivatives are easily modified to incorporate these same numerical principles. These modified recursions yield scaled ALFs and derivatives, which are then rescaled during final synthesis in Horner’s scheme. This new approach matched Clenshaw’s method for precision and effiiciency in numerical tests. Moreover, the new techniques have the benefit of simplicity, and thus ease of programming and v ersiati lity." @default.
- W831722154 created "2016-06-24" @default.
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- W831722154 date "2002-01-01" @default.
- W831722154 modified "2023-09-25" @default.
- W831722154 title "A Simple and Stable Approach to High Degree and Order Spherical Harmonic Synthesis" @default.
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- W831722154 doi "https://doi.org/10.1007/978-3-662-04709-5_43" @default.
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