相关论文: The AAAtrig algorithm for rational approximation o…
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…
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…
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…
The AAA algorithm for rational approximation is employed to illustrate applications of rational functions all across numerical analysis.
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…
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, 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…
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…
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…
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…
Computing rational minimax approximations can be very challenging when there are singularities on or near the interval of approximation - precisely the case where rational functions outperform polynomials by a landslide. We show that far…
Potential theory for rational approximation is reviewed by means of examples computed with the AAA algorithm.
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…
We present a method for dimensionally adaptive sparse trigonometric interpolation of multidimensional periodic functions belonging to a smoothness class of finite order. This method targets applications where periodicity must be preserved…
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…
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…
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…
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…
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…
Fractional differential equations (FDEs) describe subdiffusion behavior of dynamical systems. Its non-local structure requires taking into account the whole evolution history during the time integration, which then possibly causes…