3 papers
math.NA2026
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…
math.NA2026
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…
math.NA2025
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…