This paper proposes a sketching strategy based on spherical designs, which is applied to the classical spherical basis function approach for massive spherical data fitting. We conduct theoretical analysis and numerical verifications to demonstrate the feasibility of the proposed { sketching} strategy. From the theoretical side, we prove that sketching based on spherical designs can reduce the computational burden of the spherical basis function approach without sacrificing its approximation capability. In particular, we provide upper and lower bounds for the proposed { sketching} strategy to fit noisy data on spheres. From the experimental side, we numerically illustrate the feasibility of the sketching strategy by showing its comparable fitting performance with the spherical basis function approach. These interesting findings show that the proposed sketching strategy is capable of fitting massive and noisy data on spheres.

翻译：本文提出了一种基于球面设计的草图策略，并将其应用于经典球面基函数方法以处理大规模球面数据拟合。我们从理论分析和数值验证两方面论证了该草图策略的可行性。在理论层面，我们证明了基于球面设计的草图策略能够在保持逼近能力的前提下，降低球面基函数方法的计算负担。具体而言，我们为所提出的草图策略提供了拟合球面含噪数据的上界与下界。在实验层面，我们通过数值实验展示了该草图策略与球面基函数方法相当的拟合性能，从而验证了其可行性。这些有趣结果表明，所提出的草图策略能够有效拟合球面上的大规模含噪数据。