QR-based Parallel Set-Valued Approximation with Rational Functions
Numerical Analysis
2024-12-04 v2 Numerical Analysis
Abstract
In this article a fast and parallelizable algorithm for rational approximation is presented. The method, called (P)QR-AAA, is a (parallel) set-valued variant of the AAA algorithm for scalar functions. It builds on the set-valued AAA framework introduced by Lietaert, Meerbergen, P{\'e}rez and Vandereycken, accelerating it by using an approximate orthogonal basis obtained from a truncated QR decomposition. We demonstrate both theoretically and numerically this method's accuracy and efficiency. We show how it can be parallelized while maintaining the desired accuracy, with minimal communication cost.
Cite
@article{arxiv.2312.10260,
title = {QR-based Parallel Set-Valued Approximation with Rational Functions},
author = {Simon Dirckx and Karl Meerbergen and Daan Huybrechs},
journal= {arXiv preprint arXiv:2312.10260},
year = {2024}
}