AAA
The AAA algorithm for rational approximation. 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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References in zbMATH (referenced in 32 articles , 1 standard article )
Showing results 1 to 20 of 32.
Sorted by year (- An, Dong; Lin, Lin; Xu, Ze: Split representation of adaptively compressed polarizability operator (2021)
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- Trefethen, Lloyd N.; Nakatsukasa, Yuji; Weideman, J. A. C.: Exponential node clustering at singularities for rational approximation, quadrature, and PDEs (2021)
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- Berrut, J.-P.; De Marchi, S.; Elefante, G.; Marchetti, F.: Treating the Gibbs phenomenon in barycentric rational interpolation and approximation via the S-Gibbs algorithm (2020)
- Harizanov, Stanislav; Lazarov, Raytcho; Margenov, Svetozar: A survey on numerical methods for spectral space-fractional diffusion problems (2020)
- Hofreither, Clemens: A unified view of some numerical methods for fractional diffusion (2020)
- Hokanson, Jeffrey M.; Magruder, Caleb C.: ( \mathcalH_2)-optimal model reduction using projected nonlinear least squares (2020)
- Malachivskyy, P. S.; Pizyur, Ya. V.; Malachivsky, R. P.: Chebyshev approximation by a rational expression for functions of many variables (2020)