3 papers
math.NA2026
Nested QMC designs on spheres
Hao-Ning Wu, Xiaosheng Zhuang
Nested cubature rules, in which each refinement retains all previously used nodes and thus reuses earlier function evaluations, are natural in multilevel and adaptive integration.…
math.NA2026
A Survey on Spherical Designs: Existence, Numerical Constructions, and Applications
Congpei An, Xiaosheng Zhuang
This paper provides a survey of spherical designs and their applications, with a particular emphasis on the perspective of ``numerical analysis''. A set \(X_N\) of \(N\) points on…
math.NA2023
Spherical Designs for Function Approximation and Beyond
Yuchen Xiao, Xiaosheng Zhuang
In this paper, we compare two optimization algorithms using full Hessian and approximation Hessian to obtain numerical spherical designs through their variational characterization.…