周期函数的有理逼近的AAAesthetic算法
The AAAtrig algorithm for rational approximation of periodic functions
摘要：
我们提出了一个扩展的AAA（自适应Antoulas-安德森）算法的周期函数，称为“AAAtrix”。该算法使用AAA近似的关键步骤，通过（i）表示（三角）重心形式的近似和（ii）选择支持点greetly。因此，AAA 10继承了AAA的所有有利特性，因此非常灵活和鲁棒，能够考虑复平面中相当一般的样本点集合。我们考虑了一系列的应用，特别强调解决拉普拉斯方程在周期域和压缩周期共形映射。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。
英文摘要：
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 favourable 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
