Paper Info
Title
The AAA Algorithm for Rational Approximation.
Abstract
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.
Year
DOI
Venue
2018
10.1137/16M1106122
SIAM JOURNAL ON SCIENTIFIC COMPUTING
Keywords
Field
DocType
rational approximation,barycentric formula,analytic continuation,AAA algorithm,Froissart doublet,vector fitting,RKFIT
Mathematical optimization,Exponential function,MATLAB,Algebra,Mathematical analysis,Interpolation,Algorithm,Vector fitting,Rational function,Mathematics,Barycentric coordinate system
Journal
Volume
Issue
ISSN
40
3
1064-8275
Citations 
PageRank 
References 
5
0.62
11
Authors
3
Name
Order
Citations
PageRank
Yuji Nakatsukasa19717.74
Olivier Sète250.62
Lloyd N. Trefethen31024203.66