In this paper, we compare two optimization algorithms using full Hessian and approximation Hessian to obtain numerical spherical designs through their variational characterization. Based on the obtained spherical design point sets, we investigate the approximation of smooth and non-smooth functions by spherical harmonics with spherical designs. Finally, we use spherical framelets for denoising Wendland functions as an application, which shows the great potential of spherical designs in spherical data processing.

翻译：本文比较了使用完整Hessian矩阵与近似Hessian矩阵的两种优化算法，通过变分特征化方法获取数值球面设计。基于所获得的球面设计点集，我们研究了利用球面调和函数结合球面设计对光滑与非光滑函数进行逼近的方法。最后，我们将球面框架小波应用于Wendland函数去噪，展示了球面设计在球面数据处理中的巨大潜力。