9 citations · 15 across the 9 of their papers we have counts for
6 papers · 1 filter
Variable decoupling and the Kolmogorov Superposition Theorem for rational functions
A. C. Antoulas, I. V. Gosea, C. Poussot-Vassal
This work shows that for rational multivariate functions, the Kolmogorov Superposition Theorem (KST) involves several single-variable functions, which can be written down by inspec…
Rational approximation for Zolotarev sign and ratio problems
Charles Poussot-Vassal, Ion Victor Gosea, Athanasios C. Antoulas
We study algorithms for Zolotarev (3rd and 4th) problems rational approximation. First, we show that the Loewner framework (LF) is appropriate to rapidly and with no iterations, ap…
Tensor-based multivariate function approximation: methods benchmarking and comparison
Charles Poussot-Vassal, Ion Victor Gosea, Pierre Vuillemin +1
We evaluate some methods designed for tensor- (or data-) based multivariate model construction (approximation and compression). To this aim, a collection of multivariate functions…
On the Loewner framework, the Kolmogorov superposition theorem, and the curse of dimensionality
Athanasios C. Antoulas, Ion Victor Gosea, Charles Poussot-Vassal
The Loewner framework is an interpolatory approach for the approximation of linear and nonlinear systems. The purpose here is to extend this framework to linear parametric systems…
Factorization of the Loewner matrix pencil and its consequences
Qiang Zhang, Ion Victor Gosea, Athanasios C. Antoulas
This paper starts by deriving a factorization of the Loewner matrix pencil that appears in the data-driven modeling approach known as the Loewner framework and explores its consequ…
Rational approximation of the absolute value function from measurements: a numerical study of recent methods
Ion Victor Gosea, Athanasios C. Antoulas
In this work, we propose an extensive numerical study on approximating the absolute value function. The methods presented in this paper compute approximants in the form of rational…