13 citations · 48 across the 20 of their papers we have counts for
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From Pólya's Conditions to a Complete Characterization of the Convergence of Hyperinterpolation
Congpei An, Xiannan Hu, Xiaoming Yuan
It has remained open to identify the necessary and sufficient conditions for the convergence of hyperinterpolation since it was introduced by Sloan in 1995. We show that the…
An Optimization Approach to Weight Collocation for Scattered Spherical Data
Congpei An, Xiannan Hu, Xiaoming Yuan
We introduce an optimization approach for constructing spherical quadrature rules on arbitrarily scattered data. Rather than designing node placements, the new approach focuses on…
Spherical configurations and quadrature methods for integral equations of the second kind
Congpei An, Hao-Ning Wu
In this paper, we propose and analyze a product integration method for the second-kind integral equation with weakly singular and continuous kernels on the unit sphere $\mathbb{S}^…
Hybrid hyperinterpolation over general regions
Congpei An, Jiashu Ran, Alvise Sommariva
We present an -regularized discrete least squares approximation over general regions under assumptions of hyperinterpolation, named hybrid hyperinterpolation. Hybr…
Regularized Barzilai-Borwein method
Congpei An, Xin Xu
We develop a novel stepsize based on \BB method for solving some challenging optimization problems efficiently, named regularized \BB (RBB) stepsize. We indicate that RBB stepsize…
Bypassing the quadrature exactness assumption of hyperinterpolation on the sphere
Congpei An, Hao-Ning Wu
This paper focuses on the approximation of continuous functions on the unit sphere by spherical polynomials of degree via hyperinterpolation. Hyperinterpolation of degree i…
Lasso trigonometric polynomial approximation for periodic function recovery in equidistant points
Congpei An, Mou Cai
In this paper, we propose a fully discrete soft thresholding trigonometric polynomial approximation on named Lasso trigonometric interpolation. This approximation is an $…
Hard thresholding hyperinterpolation over general regions
Congpei An, Jiashu Ran
This paper proposes a novel variant of hyperinterpolation, called hard thresholding hyperinterpolation. This approximation scheme of degree leverages a hard thresholding operat…
Is hyperinterpolation efficient in the approximation of singular and oscillatory functions?
Congpei An, Hao-Ning Wu
Singular and oscillatory functions feature in numerous applications. The high-accuracy approximation of such functions shall greatly help us develop high-order methods for solving…
On the quadrature exactness in hyperinterpolation
Congpei An, Hao-Ning Wu
This paper investigates the role of quadrature exactness in the approximation scheme of hyperinterpolation. Constructing a hyperinterpolant of degree requires a positive-weight…
The springback penalty for robust signal recovery
Congpei An, Hao-Ning Wu, Xiaoming Yuan
We propose a new penalty, the springback penalty, for constructing models to recover an unknown signal from incomplete and inaccurate measurements. Mathematically, the springback p…
Lasso hyperinterpolation over general regions
Congpei An, Hao-Ning Wu
This paper develops a fully discrete soft thresholding polynomial approximation over a general region, named Lasso hyperinterpolation. This approximation is an -regularized…
Tikhonov regularization for polynomial approximation problems in Gauss quadrature points
Congpei An, Hao-Ning Wu
This paper is concerned with the introduction of Tikhonov regularization into least squares approximation scheme on by orthonormal polynomials, in order to handle noisy da…
The Numerical Stability of Regularized Barycentric Interpolation Formulae for Interpolation and Extrapolation
Congpei An, Hao-Ning Wu
The and regularized modified Lagrange interpolation formulae over are deduced in this paper. This paper mainly analyzes the numerical characteristics of…
Regularized Weighted Discrete Least Squares Approximation Using Gauss Quadrature Points
Congpei An, Hao-Ning Wu
We consider polynomial approximation over the interval by regularized weighted discrete least squares methods with or regularization, respectively. As t…
Numerical Integration over the Unit Sphere by using spherical t-design
Congpei An, Siyong Chen
This paper studies numerical integration over the unit sphere by using spherical -design, which is an equal positive weights quadrature r…
Error Bounds for Numerical Integration of Oscillatory Bessel Transforms with Algebraic or Logarithmic Singularities
Hongchao Kang, Congpei An
In this paper, we present and analyze the Clenshaw-Curtis-Filon methods for computing two classes of oscillatory Bessel transforms with algebraic or logarithmic singularities. More…