3rd Mathematics Webinar
Recent Advances on Approximation Theory
The approximation is the basis of all mathematical procedures, since the exact solutions of the problems of the applied sciences are limited to a negligible number of cases. The same real numbers, not rational, they can be conceived only for the possibility of assigning for them some approximations by default and by excess, with a consequent estimate of the error. The modern theory of approximation can be traced back to P.L. Chebyshev. His first work on approximation: "Théorie des mécanismes connus sous le nom de parallélogrammes" (1854) and the following: "Sur les questions de minima qui se rattachent à la représentation approximative des functions" (1859), began 40 years of research on approximation in connection with the theory of mechanisms. Orthogonal polynomials and special functions represent a crucial tool for approaching the modern theory of approximation. The orthogonality property is certainly the most important one to use in approximation problems, since it allows to avoid the numerical instability that occurs using the Hilbert matrix. It has been shown that the pseudo-Chebyshev functions verify this property (in the same interval and with the same weights of the corresponding classical polynomials). It is not necessary to remember the importance of the numerous families of polynomials and special functions that come used in the solutions of the most diverse problems of mathematical physics. Among these, they have great relevance the Bessel functions, recently linked to Legendre polynomials. The analysis of fractional calculus through the concepts and formalism of some class of orthogonal polynomials (in particular the Hermite polynomials) had an important development, also in relation to the large interest that this research sector has had in recent years.
Date: 10 November 2022
Time: 9:00 am CET | 3:00 am EST | 1:30 pm IST | 4:00 pm CST Asia
Webinar ID: 856 3178 1191
Webinar Secretariat: mathematics.webinar@mdpi.com