3 papers
math.NA2026
Lightning Plus Polynomial Approximation: Optimal Root-Exponential Convergence for Singular Functions in Corner Domains
Shuhuang Xiang, Jun Xiang, Shunfeng Yang +1
This paper presents a rigorous convergence analysis for the lightning plus polynomial approximation scheme, which employs rational approximations constructed with preassigned taper…
math.NA2026
Optimal asymptotic analyses on Laguerre and Hermite orthogonal approximation for functions of algebraic and logarithmic regularitiesYali
Yali Zhang, Guidong Liu, Shuhuang Xiang
Based on the Hilb-type formula and van der Corput-type lemmas, we present optimal asymptotic estimates for the decay of the Laguerre and Hermite coefficients for functions with alg…
math.NA2024
Polynomial and rational interpolation: potential, barycentric weights, and Lebesgue constants
Kelong Zhao, Shuhuang Xiang
In this paper, we focus on barycentric weights and Lebesgue constants for Lagrange interpolation of arbitrary node distributions on \([-1,1]\). The following three main works are i…