THE p-AAA ALGORITHM FOR DATA DRIVEN MODELING OF PARAMETRIC DYNAMICAL SYSTEMS

作     者：Rodriguez, Andrea Carracedo Balicki, Linus Gugercin, Serkan 

作者机构：Department of Mathematics Virginia Tech BlacksburgVA24061 United States Department of Mathematics and Computational Modeling Data Analytics Division Academy of Data Science VA24061 United States 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2020年

核心收录：

主　　题：Transfer functions 

摘      要：The AAA algorithm has become a popular tool for data-driven rational approximation of single variable functions, such as transfer functions of linear dynamical systems. In the setting of parametric dynamical systems appearing in many prominent applications, the underlying (transfer) function to be modeled is a multivariate function. With this in mind, we develop the AAA framework for approximating multivariate functions where the approximant is constructed in the multivariate barycentric form. The method is data-driven, in the sense that it does not require access to the full state-space model and requires only function evaluations. We discuss an extension to the case of matrix-valued functions, i.e., multi-input/multi-output dynamical systems, and provide a connection to the tangential interpolation theory. Several numerical examples illustrate the effectiveness of the proposed approach. Copyright © 2020, The Authors. All rights reserved.