6 papers
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…
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…
A Trust Region Method with Regularized Barzilai-Borwein Step-Size for Large-Scale Unconstrained Optimization
Xin Xu, Congpei An
We develop a Trust Region method with Regularized Barzilai-Borwein step-size obtained in a previous paper for solving large-scale unconstrained optimization problems. Simultaneousl…