SIAM Journal on Scientific Computing, Volume 43, Issue 5, Page A3372-A3392, January 2021.
We present an extension of the AAA (adaptive Antoulas--Anderson) algorithm for periodic functions, called “AAAtrig.” The algorithm uses the key steps of AAA approximation by (i) representing the approximant in (trigonometric) barycentric form and (ii) selecting the support points greedily. Accordingly, AAAtrig inherits all the favorable characteristics of AAA and is thus extremely flexible and robust, being able to consider quite general sets of sample points in the complex plane. We consider a range of applications with particular emphasis on solving Laplace's equation in periodic domains and compressing periodic conformal maps. These results reproduce the tapered exponential clustering effect observed in other recent studies. The algorithm is implemented in Chebfun.

中文翻译：

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周期函数有理逼近的AAAtrig算法

SIAM 科学计算杂志，第 43 卷，第 5 期，第 A3372-A3392 页，2021 年 1 月。
我们为周期函数提供了 AAA（自适应安图拉斯-安德森）算法的扩展，称为“AAAtrig”。该算法通过 (i) 以（三角）重心形式表示近似值和 (ii) 贪婪地选择支持点来使用 AAA 近似的关键步骤。因此，AAAtrig 继承了 AAA 的所有有利特性，因此非常灵活和健壮，能够考虑复平面中非常通用的采样点集。我们考虑了一系列应用，特别强调在周期域中求解拉普拉斯方程和压缩周期保角映射。这些结果再现了最近其他研究中观察到的锥形指数聚类效应。该算法在 Chebfun 中实现。