13 papers
Positive Cubature Compression and Optimal Hyperinterpolation Stability on a Conic Surface
Congpei An, Yan Ge
We study the computational cost and stability of positive cubature and hyperinterpolation on a truncated conic surface with a Jacobi-type weight. A classical quadratic disk-to-cone…
Exact Finite Integral Geometry: Directional Kernels and Spherical Designs
Congpei An
We study when an invariant directional average from integral geometry can be replaced exactly by finitely many directions. For an even continuous kernel , let …
Dual Geometry of Spherical Designs: Polarity, Self-Polar Rigidity, and Quadrature Structure
Congpei An
Let $X=\{x_1,\ldots,x_N\}\subset\Sph^{d-1}$ be a spherical -design, , and let be its Minkowski polytope. If , then \[ P_X^\circ=\conv\{…
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 -design of strength , and let be its empirical measure. Minkowski's theorem associates with a convex…
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…
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…
The algebraic structure of hyperinterpolation class on the sphere
Congpei An, Jiashu Ran
This paper investigates the algebraic properties of the hyperinterpolation class on the unit sphere . We focus on operators derived from…
Parameter choice strategies for regularized least squares approximation of noisy continuous functions on the unit circle
Congpei An, Mou Cai
This paper explores the incorporation of Tikhonov regularization into the least squares approximation scheme using trigonometric polynomials on the unit circle. This approach encom…