Related papers: The AAA algorithm for rational approximation
The adaptive Antoulas-Anderson (AAA) algorithm for rational approximation is a widely used method for the efficient construction of highly accurate rational approximations to given data. While AAA can often produce rational approximations…
AAA rational approximation has normally been carried out on a discrete set, typically hundreds or thousands of points in a real interval or complex domain. Here we introduce a continuum AAA algorithm that discretizes a domain adaptively as…
The AAA algorithm for rational approximation is employed to illustrate applications of rational functions all across numerical analysis.
Approximations based on rational functions are widely used in various applications across computational science and engineering. For univariate functions, the adaptive Antoulas-Anderson algorithm (AAA), which uses the barycentric form of a…
Rational approximation is a powerful tool to obtain accurate surrogates for nonlinear functions that are easy to evaluate and linearize. The interpolatory adaptive Antoulas--Anderson (AAA) method is one approach to construct such…
Rational minimax approximation of real functions on real intervals is an established topic, but when it comes to complex functions or domains, there appear to be no algorithms currently in use. Such a method is introduced here, the {\em…
A selection of algorithms for the rational approximation of matrix-valued functions are discussed, including variants of the interpolatory AAA method, the RKFIT method based on approximate least squares fitting, vector fitting, and a method…
Many algorithms for approximating data with rational functions are built on interpolation or least-squares approximation. Inspired by the adaptive Antoulas-Anderson (AAA) algorithm for the univariate case, the parametric adaptive…
The AAA algorithm, introduced in 2018, computes best or near-best rational approximations to functions or data on subsets of the real line or the complex plane. It is much faster and more robust than previous algorithms for such problems…
Potential theory for rational approximation is reviewed by means of examples computed with the AAA algorithm.
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…
We consider the problem of finding a rational function in barycentric form to approximate a given function or data set in $\mathbb{R}$ or $\mathbb{C}$. The famous AAA algorithm, introduced in 2018, constructs such a rational function: the…
The AAA algorithm has become a popular tool for data-driven rational approximation of single variable functions, such as transfer functions of a linear dynamical system. In the setting of parametric dynamical systems appearing in many…
We propose AAA rational approximation as a method for interpolating or approximating smooth functions from equispaced data samples. Although it is always better to approximate from large numbers of samples if they are available, whether…
We present two new methods for multivariate exponential analysis. In [7], we developed a new algorithm for reconstruction of univariate exponential sums by exploiting the rational structure of their Fourier coefficients and reconstructing…
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.,…
We introduce a theoretical framework for the rational approximation of optical response functions in resonant photonic systems. The framework is based on the AAA algorithm and further allows to solve the underlying nonlinear eigenproblems…
We consider the Adaptive Antoulas-Anderson (AAA) rational interpolation algorithm recently developed by Trefethen and co-authors, which can be viewed as a type of moment-matching technique for system realization and approximation. We…
In this article a fast and parallelizable algorithm for rational approximation is presented. The method, called (P)QR-AAA, is a (parallel) set-valued variant of the AAA algorithm for scalar functions. It builds on the set-valued AAA…
Rational approximation appears in many contexts throughout science and engineering, playing a central role in linear systems theory, special function approximation, and many others. There are many existing methods for solving the rational…