5 papers
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…
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…
Rational approximation for Zolotarev sign and ratio problems
Athanasios C. Antoulas, Ion Victor Gosea, Charles Poussot-Vassal
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…
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…
Structure-Preserving Discretization and Model Order Reduction of Boundary-Controlled 1D Port-Hamiltonian Systems
Jesus-Pablo Toledo-Zucco, Denis Matignon, Charles Poussot-Vassal +1
This paper presents a systematic methodology for the discretization and reduction of a class of one-dimensional Partial Differential Equations (PDEs) with inputs and outputs colloc…