论文标题
通过测量值的绝对值函数的合理近似：最近方法的数值研究
Rational approximation of the absolute value function from measurements: a numerical study of recent methods
论文作者
论文摘要
在这项工作中，我们提出了一项有关近似绝对值函数的广泛数值研究。本文提出的方法以有理函数的形式计算近似值，并已相对较最近提出，例如Loewner框架和AAA算法。此外，这些方法基于数据，即原始函数的测量（因此是数据驱动的性质）。我们将这两种方法的数值结果与最近提供的最佳理性近似方法（Minimax算法）以及上一个世纪的各种经典界限进行了比较。最后，我们提出了Loewner框架的迭代扩展，可用于提高理性近似值的近似质量。
In this work, we propose an extensive numerical study on approximating the absolute value function. The methods presented in this paper compute approximants in the form of rational functions and have been proposed relatively recently, e.g., the Loewner framework and the AAA algorithm. Moreover, these methods are based on data, i.e., measurements of the original function (hence data-driven nature). We compare numerical results for these two methods with those of a recently-proposed best rational approximation method (the minimax algorithm) and with various classical bounds from the previous century. Finally, we propose an iterative extension of the Loewner framework that can be used to increase the approximation quality of the rational approximant.
