Work

$L^2$ and $L^\infty$ rational approximation

Year: 2025

Type: preprint

Abstract: Using recently developed algorithms, we compute and compare best $L^2$ and $L^\infty$ 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 $L^2$ best approximations, we employ a new formulation of TF-IRKA in barycentric form.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2512.23357

Authors: Ackermann, Michael S., Reiter, Sean, Trefethen, Lloyd N.

Institutions: Virginia Tech, Courant Institute of Mathematical Sciences, New York University, Harvard University

Topic: Mathematical functions and polynomials

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7117781945

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