Hermite-Pad\'{e} approximation, multiple orthogonal polynomials, and multidimensional Toda equations
Exactly Solvable and Integrable Systems
2023-10-27 v2 Numerical Analysis
Mathematical Physics
Classical Analysis and ODEs
math.MP
Numerical Analysis
Abstract
We review recent results on the connection between Hermite-Pad\'e approximation problem, multiple orthogonal polynomials, and multidimensional Toda equations in continuous and discrete time. In order to motivate interest in the subject we first present a pedagogical introduction to the classical, by now, relation between the Pad\'e approximation problem, orthogonal polynomials, and the Toda lattice equations. We describe also briefly generalization of the connection to the interpolation problems and to the non-commutative algebra level.
Keywords
Cite
@article{arxiv.2310.15116,
title = {Hermite-Pad\'{e} approximation, multiple orthogonal polynomials, and multidimensional Toda equations},
author = {Adam Doliwa},
journal= {arXiv preprint arXiv:2310.15116},
year = {2023}
}
Comments
22 pages, XL Workshop on Geometric Methods in Physics, Bia{\l}owie\.za 2023; typos corrected v2