论文标题
用于周期函数合理近似的AAATRIG算法
The AAAtrig algorithm for rational approximation of periodic functions
论文作者
论文摘要
我们提出了用于周期功能的AAA（自适应Antoulas-Anderson）算法的扩展，称为“ Aaatrig”。该算法通过（i）代表（三角）barycentric形式的近似值和（ii）选择贪婪的支持点，使用AAA近似的关键步骤。因此，Aaatrig继承了AAA的所有有利特征，因此非常灵活和稳健，能够考虑复杂平面中的相当一般的样本点集。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并压缩周期性的保形图。这些结果再现了在其他最近的研究中观察到的锥形指数聚类效应。该算法在Chebfun实施。
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.
