Abstract : The numerical computation of rational approximations has become much easier since the appearance of the AAA
algorithm in 2018. This minisymposium will explore some of the many things that have happened since then.
Abstract : The AAA ("triple A") algorithm is a fast and reliable black box algorithm for computing rational approximations to real or complex functions. It has been used by many people since its publication in 2018. This talk will be an introduction to to AAA and its applications.
[05528] pAAA for multivariate functions and AAA-LQO for systems with quadratic outputs
Format : Online Talk on Zoom
Author(s) :
Serkan Gugercin (Virginia Tech)
Abstract : We first introduce the parametric-AAA (pAAA) algorithm for approximating multivariate functions, such as the transfer functions of parametric dynamical systems, where the approximant is constructed in the multivariate barycentric form. We then develop the barycentric form for linear dynamical systems with quadratic outputs (LQO). This new formulation leads to the AAA-LQO algorithm.
[02708] Rational approximation for noisy data
Format : Talk at Waseda University
Author(s) :
Anil Damle (Cornell University)
Abstract : Approximation of data by rational functions has many clear upsides over other representational forms. However, even if a rational function provides an effective underlying model for a given task the data it must be built from is often corrupted by noise. In this talk we will explore how existing rational approximation algorithms are impacted by noise, and discuss algorithms that are specifically tailored to effectively and efficiently build rational approximations of noisy data.
[03138] SO-AAA: learning systems with second-order dynamics
Format : Talk at Waseda University
Author(s) :
Ion Victor Gosea (Max Planck Institute for Dynamics of Complex Technical Systems)
Serkan Gugercin (Virginia Tech University)
Steffen W. R. Werner (New York University)
Abstract : The AAA (Adaptive Antoulas Anderson) algorithm is a rational approximation tool used to fit rational functions to data measurements. We present here an extension of AAA to fi tting systems with second-order dynamics (structured case). Toward this goal, the development of structured barycentric forms associated with the transfer function of second-order systems is needed. These allow the iterative construction of reduced-order models from given frequency domain data, by combining interpolation and least-squares fi t.
[02698] Linearization of dynamical systems using the AAA algorithm
Format : Talk at Waseda University
Author(s) :
Karl Meerbergen (KU Leuven)
Abstract : We provide an overview of the use of AAA for the linearization of all kinds of nonlinear equations arising from dynamical systems. This includes nonlinear eigenvalue problems, nonlinear frequency dependent dynamical systems and nonlinear time dependent systems. The concept linearization is key for these problems, since linear problems are usually easier to handle in numerics.
[02371] Time-domain model reduction in the Loewner framework
Format : Talk at Waseda University
Author(s) :
Athanasios Antoulas (Rice University)
Abstract : In this talk we will present the main features of the Loewner Framework for rational approximation and model reduction. In particular, time domain methods will be of central importance.
[05435] AAA and numerical conformal mapping
Format : Online Talk on Zoom
Author(s) :
Olivier Sète (University of Greifswald)
Abstract : In this talk, we explore applications of AAA rational approximation in numerical conformal mapping.
[05536] AAA rational approximation on a continuum
Format : Talk at Waseda University
Author(s) :
Yuji Nakatsukasa (University of Oxford)
Abstract : AAA has normally been applied on a discrete set, typically hundreds or thousands of points in a (real or complex) domain. Here we introduce a continuum AAA algorithm that discretizes a domain adaptively as it goes, which often also reduces the number of samples required. The key idea is that the support points tend to indicate where more samples are required. Execution is fast since SVDs are computed only for matrices that are nearly square.
