Spherical designs for function approximation and beyond

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...

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Bibliographic Details
Published inSampling theory, signal processing, and data analysis Vol. 23; no. 2
Main Authors Xiao, Yuchen, Zhuang, Xiaosheng
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.12.2025
Subjects
Abstract Harmonic Analysis
Machine Learning
Mathematics
Mathematics and Statistics
Original Article
Signal,Image and Speech Processing
Wendland functions
58C35
Function approximation
Spherical
Trust region
42C40
Restart conjugate gradient
65D32
design
Variational characterization
Spherical harmonic transforms
Spherical framelets
42C15
65D18
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Summary: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.
ISSN:2730-5716
2730-5724
DOI:10.1007/s43670-025-00105-4