19-23 June 2023
Faculty of Physics, University of Warsaw
Europe/Warsaw timezone
Rational interpolation/approximation and integrability
Presented by Prof. Adam DOLIWA
on
23 Jun 2023
from
09:45
to
10:15
Content
It is well known that the rational (or Padé) approximants are closely related with the discrete-time Toda equation. The structural connection with orthogonal polynomials provides a link between the theory of integrable systems and various classical results of applied mathematics and numerical analysis. Inspired by recent advances on symmetry and integrability of difference equations I would like to disuss several generalizations of the relation (some of them already known):
* the role of Hirota's discrete KP system;
* non-commutative versions of the classical results;
* approximation as a confluent limit of the interpolation.
[1] A. Doliwa, A. Siemaszko, Integrability and geometry of the Wynn recurrence, Numer. Algorithms doi: 10.1007/s11075-022-01344-5
[2] A. Doliwa, A. Siemaszko, Hermite-Padé approximation and integrability, arXiv:2201.06829
[3] A. Doliwa, Non-commutative Hermite-Padé approximation and integrability, Lett. Math. Phys. 112 68 (2022) doi: 10.1007/s11005-022-01560-z
[4] A. Doliwa, Non-autonomous multidimensional Toda system and multiple interpolation problem, J. Phys. A: Math. Theor. 55 (2022) 505202 (17 pp.) doi: 10.1088/1751-8121/acad4d
Place
Location: Faculty of Physics, University of Warsaw
Address: Pasteura 5, Warsaw
Room: Lecture hall: 0.06