An Algorithm for Real and Complex Rational Minimax Approximation
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Publication:5132009
DOI10.1137/19M1281897zbMATH Open1452.65035arXiv1908.06001MaRDI QIDQ5132009
Author name not available (Why is that?)
Publication date: 9 November 2020
Published in: (Search for Journal in Brave)
Abstract: Rational minimax approximation of real functions on real intervals is an established topic, but when it comes to complex functions or domains, there appear to be no algorithms currently in use. Such a method is introduced here, the {em AAA-Lawson algorithm,} available in Chebfun. The new algorithm solves a wide range of problems on arbitrary domains in a fraction of a second of laptop time by a procedure consisting of two steps. First, the standard AAA algorithm is run to obtain a near-best approximation and a set of support points for a barycentric representation of the rational approximant. Then a "Lawson phase" of iteratively reweighted least-squares adjustment of the barycentric coefficients is carried out to improve the approximation to minimax.
Full work available at URL: https://arxiv.org/abs/1908.06001
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