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Main Authors: Xiao, Yuchen, Zhuang, Xiaosheng
Format: Preprint
Published: 2023
Subjects:
Online Access:https://arxiv.org/abs/2311.18333
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author Xiao, Yuchen
Zhuang, Xiaosheng
author_facet Xiao, Yuchen
Zhuang, Xiaosheng
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2311_18333
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Spherical Designs for Function Approximation and Beyond
Xiao, Yuchen
Zhuang, Xiaosheng
Numerical Analysis
Signal Processing
42C05, 58C35, 65K10, 65D15, 65D32
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.
title Spherical Designs for Function Approximation and Beyond
topic Numerical Analysis
Signal Processing
42C05, 58C35, 65K10, 65D15, 65D32
url https://arxiv.org/abs/2311.18333