Related papers: Pad\'e Approximation and Hypergeometric Functions:…
We study the properties of stochastic approximation applied to a tame nondifferentiable function subject to constraints defined by a Riemannian manifold. The objective landscape of tame functions, arising in o-minimal topology extended to a…
Pad\'e approximation has two natural extensions to vector rational approximation through the so called type I and type II Hermite-Pad\'e approximants. The convergence properties of type II Hermite-Pad\'e approximants have been studied. For…
This article revisits the approximation problem of systems of nonlinear delay differential equations (DDEs) by a set of ordinary differential equations (ODEs). We work in Hilbert spaces endowed with a natural inner product including a point…
The pseudospectra of a linear time-invariant system are the sets in the complex plane consisting of all the roots of the characteristic equation when the system matrices are subjected to all possible perturbations with a given upper bound.…
The advantages and difficulties of application of Pad\'e approximants to two-dimensional regression analysis are discussed. New formulation of residuals is suggested in the method of least squares. It leads to a system of linear equations…
We investigate singular perturbation problems caused by small delays in the view of pseudo-exponential dichotomy. For a general linear non-autonomous retarded differential equation with small delay, previous works established the existence…
Parametric partial differential equations (PDEs) are fundamental for modeling a wide range of physical and engineering systems influenced by uncertain or varying parameters. Traditional neural network-based solvers, such as Physics-Informed…
For many optimization problems it is possible to define a distance metric between problem variables that correlates with the likelihood and strength of interactions between the variables. For example, one may define a metric so that the…
We consider a system of fermions with local interactions on a lattice (Hubbard model) and apply a novel extension of the Laplace's method (saddle-point approximation) for evaluating the corresponding partition function. There, we introduce…
This paper introduces a novel error estimator for the Proper Generalized Decomposition (PGD) approximation of parametrized equations. The estimator is intrinsically random: It builds on concentration inequalities of Gaussian maps and an…
We describe how to solve simultaneous Pad\'e approximations over a power series ring $K[[x]]$ for a field $K$ using $O~(n^{\omega - 1} d)$ operations in $K$, where $d$ is the sought precision and $n$ is the number of power series to…
Partial differential equations with discrete (concentrated) state-dependent delays in the space of continuous functions are investigated. In general, the corresponding initial value problem is not well posed, so we find an additional…
In this paper, we propose a general approach for approximate simulation and analysis of delay differential equations (DDEs) with distributed time delays based on methods for ordinary differential equations (ODEs). The key innovation is that…
This paper studies equality-constrained composite minimization problems. This class of problems, capturing regularization terms and inequality constraints, naturally arises in a wide range of engineering and machine learning applications.…
We apply the technique of self-similar exponential approximants based on successive truncations of continued exponentials to reconstruct functional laws of the quasi-exponential class from the knowledge of only a few terms of their power…
Delay differential equations take into account the transmission time of the information. These delayed signals may turn a predictable system into chaotic, with the usual fractalization of the phase space. In this work, we study the…
This article serves as an introduction to several recent developments in the study of quasisymmetric functions. The focus of this survey is on connections between quasisymmetric functions and the combinatorial Hopf algebra of noncommutative…
Recently, Meta-Auto-Decoder (MAD) was proposed as a novel reduced order model (ROM) for solving parametric partial differential equations (PDEs), and the best possible performance of this method can be quantified by the decoder width. This…
En utilisant des approximants de Hermite-Pad\'e de fonctions exponentielles, ainsi que des d\'eterminants d'interpolation de Laurent, nous minorons la distance entre un nombre alg\'ebrique et l'exponentielle d'un nombre alg\'ebrique non…
Stochastic gradient descent (SGD) and its variants have established themselves as the go-to algorithms for large-scale machine learning problems with independent samples due to their generalization performance and intrinsic computational…