Journal
SIAM JOURNAL ON SCIENTIFIC COMPUTING
Volume 40, Issue 3, Pages A1494-A1522Publisher
SIAM PUBLICATIONS
DOI: 10.1137/16M1106122
Keywords
rational approximation; barycentric formula; analytic continuation; AAA algorithm; Froissart doublet; vector fitting; RKFIT
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Funding
- Japan Society for the Promotion of Science
- European Research Council under the European Union's Seventh Framework Programme (FP7)/ERC [291068]
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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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