A fast algorithm for expansion over spherical harmonics
A usual way to obtain algorithms for expansion over spherical harmonics is to use an integration method over some grid on the unit sphere. From the author's abstract: ``We provide an algorithm of complexity \(O(NL \log^2L)\) for multiplication of the matrix of values of spherical harmonics in points of an arbitrary grid on the unit sphere. The algorithm is based on interrelation between spherical harmonics and Legendre polynomials and on a fast algorithm for expansion over Legendre polynomials''. Here \(N\) stands for the number of the grid points and \(L\) is the maximal degree of the spherical harmonics involved.
scientific article; zbMATH DE number 817201