$L^2$ and $L^\infty$ rational approximation
Numerical Analysis
2025-12-30 v1 Numerical Analysis
Complex Variables
Abstract
Using recently developed algorithms, we compute and compare best and rational approximations of analytic functions on the unit disk. Although there is some theory for these problems going back decades, this may be the first computational study. To compute the best approximations, we employ a new formulation of TF-IRKA in barycentric form.
Cite
@article{arxiv.2512.23357,
title = {$L^2$ and $L^\infty$ rational approximation},
author = {Michael S. Ackermann and Sean Reiter and Lloyd N. Trefethen},
journal= {arXiv preprint arXiv:2512.23357},
year = {2025}
}