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Spherical Designs for Function Approximation and Beyond

2023/11/30 by Yuchen Xiao, Xiao, Yuchen, Xiaosheng Zhuang +1
Computer Science · Engineering · #3D Shape Modeling and Analysis #42C05 #58C35 #65D15 #65D32 #65K10 #Advanced Numerical Analysis Techniques #FOS: Electrical engineering #FOS: Mathematics #Numerical Analysis (math.NA) #Optical measurement and interference techniques #Signal Processing (eess.SP) #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.2311.18333

openalex publication_date 2023/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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