7 papers · 1 filter
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…
On the role of weak Marcinkiewicz-Zygmund constants in polynomial approximation by orthogonal bases
Congpei An, Alvise Sommariva, Marco Vianello
We compute numerically the Marcinkiewicz-Zygmund constants of cubature rules, with a special attention to their role in polynomial approximation by orthogonal bases. We test…
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…
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…
Recovery Thresholding Hyperinterpolations in Signal Processing
Congpei An, Jiashu Ran
This paper introduces recovery thresholding hyperinterpolations, a novel class of methods for sparse signal reconstruction in the presence of noise. We develop a framework that int…
Quasi-Monte Carlo hyperinterpolation
Congpei An, Mou Cai, Takashi Goda
This paper studies a generalization of hyperinterpolation over the high-dimensional unit cube. Hyperinterpolation of degree \( m \) serves as a discrete approximation of the \( L_2…