English

$L^2$ 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 L2L^2 and LL^\infty 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 L2L^2 best approximations, we employ a new formulation of TF-IRKA in barycentric form.

Keywords

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}
}
R2 v1 2026-07-01T08:44:08.102Z