Congpei An

collaborators

9 papers

math.MG2026

Minkowski Polytopes of Spherical Designs: High-Order Isotropy and Quantitative Sphericity

Congpei An

Let $X_N=\{x_1,\dots,x_N\}\subset \Sph^2$ be a spherical $t$ -design of strength $t \geq 2$ , and let $μ_{X}$ be its empirical measure. Minkowski's theorem associates with $X_{N}$ a convex…

math.NA2026

How many integrals should be evaluated at least in two-dimensional hyperinterpolation?

Maolin Che, Congpei An, Yimin Wei +1

This paper introduces a novel approach to approximating continuous functions over high-dimensional hypercubes by integrating matrix CUR decomposition with hyperinterpolation techni…

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.NA2026

On the role of weak Marcinkiewicz-Zygmund constants in polynomial approximation by orthogonal bases

Congpei An, Alvise Sommariva, Marco Vianello

We compute numerically the $L^{2}$ Marcinkiewicz-Zygmund constants of cubature rules, with a special attention to their role in polynomial approximation by orthogonal bases. We test…

math.NA2025

The path of hyperinterpolation: A survey

Congpei An, Jiashu Ran, Hao-Ning Wu

This paper surveys hyperinterpolation, a quadrature-based approximation scheme. We cover classical results, provide examples on several domains, review recent progress on relaxed q…

math.FA2025

The algebraic structure of hyperinterpolation class on the sphere

Congpei An, Jiashu Ran

This paper investigates the algebraic properties of the hyperinterpolation class $HC (S^{d})$ on the unit sphere $S^{d}$ . We focus on operators derived from…