Distributed Filtered Hyperinterpolation for Noisy Data on the Sphere

Problems in astrophysics, space weather research, and geophysics usually need to analyze big noisy data on the sphere. This paper develops distributed filtered hyperinterpolation for sphere, which assigns fitting task multiple servers find a good approximation of mapping input output data. For each server, is sphere by small proportion quadrature nodes. The strategy allows parallel computing processing model selection. It reduces computational cost server while preserving capability compared hyperinterpolation. We prove quantitative relation between numbers servers. Numerical examples show efficiency accuracy proposed method.