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The AAA algorithm for rational approximation
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The AAA algorithm for rational approximation
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We introduce a new algorithm for approximation by rational functions on a real or complex set of points, implementable in 40 lines of Matlab and requiring no user input parameters. Even on a disk or interval the algorithm may outperform existing methods, and on more complicated domains it is especially competitive. The core ideas are (1) representation of the rational approximant in barycentric form with interpolation at certain support points and (2) greedy selection of the support points to avoid exponential instabilities. The name AAA stands for "adaptive Antoulas--Anderson" in honor of the authors who introduced a scheme based on (1). We present the core algorithm with a Matlab code and nine applications and describe variants targeted at problems of different kinds. Comparisons are made with vector fitting, RKFIT, and other existing methods for rational approximation.
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Cited by 1 Pith paper
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Three-body unitary determination of the $f_1(1285)$ and $f_1(1420)$ pole positions
Fitting a spectator-isobar three-body unitary amplitude to BESIII K0S K0S pi0 data yields poles at (1277±2±1)-i(12±1±0) MeV for f1(1285) and (1435±2±7)-i(40±2±1) MeV for f1(1420), with the latter traced to a K Kbar* q...
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