Technical Report Number
Earlier work by Driscoll and Healy has produced an efficient algorithm for computing the Fourier transform of band-limited functions on the sphere. In this paper we present a greatly improved inverse transform, and consequent improved convolution algorithm for such functions. We also discuss implementational considerations and give heuristics for allowing reliable floating point implementations of a slightly modified algorithm at little cost in either theoretical or actual performance. This discussion is supplemented with numerical experiments from our implementation in C on a DecStation 5000. These results give strong indications that the algorithm is both reliable and efficient for a large range of useful problem sizes.
Dartmouth Digital Commons Citation
Healy, D M. Jr; Moore, S S. B.; and Rockmore, D, "Efficiency and Stability Issues in the Numerical Computation of Fourier Transforms and Convolutions on the 2-Sphere" (1994). Computer Science Technical Report PCS-TR94-222. https://digitalcommons.dartmouth.edu/cs_tr/95