THE AAA ALGORITHM FOR RATIONAL APPROXIMATION
THE AAA ALGORITHM FOR RATIONAL APPROXIMATION
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DOI：
10.1137/16m1106122
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发表时间：
2018-01-01
影响因子：
3.1
通讯作者：
Trefethen, Lloyd N.
中科院分区：
文献类型：
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作者：
Nakatsukasa, Yuji;Sete, Olivier;Trefethen, Lloyd N.
我们介绍了一种新的算法，通过有理函数在实数或复数点上逼近，可在40行MATLAB中实现，不需要用户输入参数。即使在磁盘或间隔上，该算法也可能优于现有的方法，在更复杂的领域中，它尤其具有竞争力。其核心思想是(1)在某些支撑点上以质心形式插值表示有理逼近；(2)贪婪选择支撑点以避免指数不稳定性。AAA的名称代表“adaptive Antoulas-Anderson”，以纪念引入基于(1)的方案的作者。我们给出了核心算法的MATLAB代码和九种应用，并描述了针对不同类型问题的变体。并与矢量拟合、RKFIT和其他现有的有理逼近方法进行了比较。
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.