Seminario sobre Polinomios Ortogonales

El Grupo de Teoría de Aproximación y Polinomios Ortogonales organiza el Seminario cuyos datos se detallan a continuación:

Fecha: Viernes, 15 de marzo de 2013
Lugar: Aula A-26 de la Facultad de Ciencias, Universidad de Granada

Edge Detection and Orthogonal  Polynomials

Sesión 12:00. Daniel Rivero, Departamento de Matemáticas, UC3M.

Resumen: Discrete orthogonal polynomials are useful tools in digital image processing to extract visual object contours in different application contexts. This paper proposes a method that extends beyond classic first-order differential operators, by using the properties of Hahn orthogonal polynomials and analysis of zero crossings to achieve a second order differential operator with higher order precision. The novel aspects of this research work are twofold: Theoretically, it is demonstrated that Hahn Polynomials provide a better approximation to the second derivative directional  than the widely used discrete Chebyshev orthogonal polynomials. Experimentally, we provide simulation results which prove that the proposed method  achieves superior performance in comparison with commonly used algorithms.

On linearly related orthogonal polynomials in several variables

Sesión 13:00. Teresa E. Pérez, Departamento de Matemática Aplicada, UGR.

Resumen: Given two monic polynomial systems in several variables satisfying a matrix linear relation, we study two problems. First, if both polynomial systems are orthogonal, to characterise when that linear relation exists in terms of their moment functionals. Second, if one of the polynomial systems is orthogonal, to study when the other one is also orthogonal. Finally, some non trivial examples are presented, as well as linear relations between adjacent families of multivariate classical orthogonal polynomials.
This is a joint work with M. Alfaro, A. Peña, and M. L. Rezola.