Applications of QR-based Vector-Valued Rational Approximation

TL;DR

This paper demonstrates the versatility and practical effectiveness of the QR-AAA algorithm in various computational applications involving vector-valued rational approximation, including fluid dynamics, quadrature, and boundary element methods.

Contribution

It introduces and applies the QR-AAA algorithm to multiple computational problems, showcasing its flexibility and efficiency in practical scenarios.

Findings

Effective in Stokes flow computation

Versatile in multivariate rational approximation

Enhances boundary element method accuracy

Abstract

Several applications of the QR-AAA algorithm, a greedy scheme for vector-valued rational approximation, are presented. The focus is on demonstrating the flexibility and practical effectiveness of QR-AAA in a variety of computational settings, including Stokes flow computation, multivariate rational approximation, function extension, the development of novel quadrature methods and near-field approximation in the boundary element method.