Related papers: The first five years of the AAA algorithm
We present a novel application of the recently developed AAA algorithm to the solution of Laplace 2D problems; an application to conformal mapping is also shown as a particular case. These classes of problems have also been addressed by…
A two-step method for solving planar Laplace problems via rational approximation is introduced. First complex rational approximations to the boundary data are determined by AAA approximation, either globally or locally near each corner or…
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…
The AAA algorithm for rational approximation is employed to illustrate applications of rational functions all across numerical analysis.
We introduce a new algorithm for approximation by rational functions on a real or complex set of points, implementable in 40 lines of Matlab and requiring no user input parameters. Even on a disk or interval the algorithm may outperform…
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…
Potential theory for rational approximation is reviewed by means of examples computed with the AAA algorithm.
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…
Unitary best approximation to the exponential function on an interval on the imaginary axis has been introduced recently. In the present work two algorithms are considered to compute this best approximant: an algorithm based on rational…
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…
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…
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…
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…
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…
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…
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…
In recent years, many design automation methods have been developed to routinely create approximate implementations of circuits and programs that show excellent trade-offs between the quality of output and required resources. This paper…
The traditional view in numerical conformal mapping is that once the boundary correspondence function has been found, the map and its inverse can be evaluated by contour integrals. We propose that it is much simpler, and 10-1000 times…
Unlike polynomials, rational functions can represent functions having poles or branch cuts with root-exponential convergence and no Runge phenomenon. Recent developments of the AAA and greedy Thiele algorithms have sparked renewed interest…
Approximate Bayesian computation (ABC) has advanced in two decades from a seminal idea to a practically applicable inference tool for simulator-based statistical models, which are becoming increasingly popular in many research domains. The…