Summary
This paper discusses a method to approximate an integral over the (unit) sphere by a linear combination of the values of the integrand at given points. The main concept of this method is the observation, that on the sphere for each sufficiently smooth function the integral can be expressed by a summation formula. A method is given for optimizing the accuracy of the computation for a given set of sample points for the function being integrated.
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Freeden, W. An application of a summation formula to numerical computation of integrals over the sphere. Bull. Geodesique 52, 165–175 (1978). https://doi.org/10.1007/BF02521770
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DOI: https://doi.org/10.1007/BF02521770