15 citations · 59 across the 16 of their papers we have counts for
8 papers · 1 filter
Breaking quadrature exactness: A spectral method for the Allen--Cahn equation on spheres
Hao-Ning Wu, Xiaoming Yuan
We present a novel spectral method for the Allen-Cahn equation on spheres, eliminating the reliance on conventional quadrature exactness conditions. By replacing these conditions w…
A Uniquely Solvable, Positivity-Preserving and Unconditionally Energy Stable Numerical Scheme for the Functionalized Cahn-Hilliard Equation with Logarithmic Potential
Wenbin Chen, Jianyu Jing, Hao Wu
We propose and analyze a first-order finite difference scheme for the functionalized Cahn-Hilliard (FCH) equation with a logarithmic Flory-Huggins potential. The semi-implicit nume…
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…