[00185] AAA rational approximation: extensions and applications
Session Date & Time :
00185 (1/2) : 4C (Aug.24, 13:20-15:00)
00185 (2/2) : 4D (Aug.24, 15:30-17:10)
Type : Proposal of Minisymposium
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.
[02371] Time-domain model reduction in the Loewner framework
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.
[02698] Linearization of dynamical systems using the AAA algorithm
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.
[02708] Rational approximation for noisy data
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
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.
[05435] AAA and numerical conformal mapping
Author(s) :
Olivier Sète (University of Greifswald)
Abstract : In this talk, we explore applications of AAA rational approximation in numerical conformal mapping.
