SIAM Journal on Numerical Analysis, Volume 59, Issue 2, Page 634-659, January 2021.
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 noisy data on the sphere, which assigns the data fitting task to multiple servers to find a good approximation of the mapping of input and output data. For each server, the approximation is a filtered hyperinterpolation on the sphere by a small proportion of quadrature nodes. The distributed strategy allows parallel computing for data processing and model selection. It reduces computational cost for each server while preserving the approximation capability compared to the filtered hyperinterpolation. We prove a quantitative relation between the approximation capability of distributed filtered hyperinterpolation and the numbers of input data and servers. Numerical examples show the efficiency and accuracy of the proposed method.

中文翻译：

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球形噪声数据的分布式滤波超插值

SIAM数值分析学报，第59卷，第2期，第634-659页，2021年1月。
天体物理学，空间天气研究和地球物理学中的问题通常需要分析球体上的大噪声数据。本文针对球面上的噪声数据开发了分布式滤波超插值算法，该算法将数据拟合任务分配给多个服务器，以找到输入和输出数据映射的良好近似值。对于每台服务器，近似值是球体上一小部分正交节点的滤波超插值。分布式策略允许并行计算以进行数据处理和模型选择。与过滤的超插值相比，它在保留逼近能力的同时降低了每台服务器的计算成本。我们证明了分布式滤波超插值的逼近能力与输入数据和服务器数量之间的定量关系。