27th Conference of the International Linear Algebra Society (ILAS 2026)

p-set valued AAA for parametric model order reduction.

May 19, 2026, 2:50 PM

25m

Torgersen Hall 1040 (Virginia Tech)

Minisymposium Talk Rational Approximation and Interpolation: Practical Applications, Challenges and Solutions Rational Approximation and Interpolation: Practical Applications, Challenges and Solutions

Speaker

Karl Meerbergen (KU Leuven)

Description

We present an extension of the AAA algorithm, named psvAAA. This MOR method combines the multivariate pAAA and uni-variate set valued AAA method. Many physical systems are described by dynamical systems with physical or geometrical parameters. Often, the system's output is strongly dependent on the Laplace variable or the frequency, and less strong on the parameters. In this talks, we present a combination of (p)AAA and set-valued AAA. The 'set' is an ensemble of frequency dependent functions evaluated in points in the parameter domain. This set is used to choose support points. In the talk, we describe ways to determine the weights and derive reduced models for evaluation in frequency or time domain.