4 papers · 1 filter
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…
Exact convergence rates of lightning plus polynomial approximation for branch singularities with uniform exponentially clustered poles
Shuhuang Xiang, Yanghao Wu, Shunfeng Yang
This paper builds rigorous analysis on the root-exponential convergence for the lightning schemes via rational functions in approximating corner (branch) singularity problems with…
The root-exponential convergence of lightning plus polynomial approximation on corner domains
Shuhuang Xiang, Shunfeng Yang
This paper builds further rigorous analysis on the root-exponential convergence for lightning schemes approximating corner singularity problems. By utilizing Poisson summation form…
On the best convergence rates of lightning plus polynomial approximations
Shuhuang Xiang, Shunfeng Yang, Yanghao Wu
Building on introducing exponentially clustered poles, Trefethen and his collaborators introduced lightning algorithms for approximating functions of singularities. These schemes m…