Charlas plenarias

Por orden alfabético:

María José Cantero (Universidad de Zaragoza, España)
Título: TBA.
Abstract: TBA.

Alfredo Deaño (University of Kent, United Kingdom)
Título: TBA.
Abstract: TBA.

Diego Dominici (State University of New York at New Paltz, USA)
Título: TBA.
Abstract: TBA.

Ulises Fidalgo (Case Western Reserve University, USA)
Título: Non complete interpolatory quadrature rules.
Abstract: Non-complete interpolatory quadrature rules were introduced in the 90's by Bloom, Lubinsky, and Stahl. With this type of rules we can compute approximation of integrals with Riemann integrable functions, where the evaluation nodes distribution has an appreciable flexibility. In this context we find a wide family of convergent schemes of nodes. To this end we use some results on the orthogonal polynomial theory, such as: strong asymptotic behavior of orthogonal polynomial with respect to varying measures, and the Wendroff theorem.

Ana Foulquié Moreno (Universidad de Aveiro, Portugal)
Título: TBA.
Abstract: TBA.

Judit Mínguez (Universidad de La Rioja, España)
Title: TBA.
Abstract: TBA

Maria das Neves Rebocho (Universidade da Beira Interior, Portugal)
Title: TBA.
Abstract: TBA

Javier Segura (Universidad de Cantabria, España)
Título: Numerical computation of classical Gaussian quadrature rules.
Abstract: The numerical computation of classical Gaussian quadrature rules has recently received a considerable attention, particularly regarding the computation of high degree rules. Most of the numerical methods are based on a combination of simple asymptotic methods for computing first estimations of the nodes, an iterative refinement of these nodes and the computation of the weights using well-known expressions derived from the Christoffel-Darboux formula. We show that direct asymptotic methods are enough for a fast and high accuracy computation of Gauss-Hermite, Gauss-Laguerre and Gauss-Jacobi quadratures, without recourse to iterative methods. And, on the other hand, we also show that it is possible to build rapidly convergent iterative methods which do not depend on asymptotics. These two separated techniques have a number advantages with respect to mixed methods: purely asymptotic methods are very fast and accurate for large degrees, while our iterative methods are valid without practical restrictions on the parameters and with arbitrary accuracy.

Jan Felipe Van Diejen (Universidad de Talca, Chile)
Título: Quadrature rules from finite orthogonality relations for Bernstein-Szegö polynomials.
Abstract: By gluing two families of Bernstein-Szegö polynomials, we construct  the eigenbasis of an associated finite-dimensional Jacobi matrix. This  gives rise to finite orthogonality relations for this composite  eigenbasis of Bernstein-Szegö polynomials. As an application, a number  of Gauss-type quadrature rules are derived for the exact integration  of rational functions with prescribed poles against the Chebyshev  weight functions. Based on work in collaboration with Erdal Emsiz  (Pontificia Universidad Católica de Chile).

Luis Verde Star (Universidad Autónoma Metropolitana, México)
Título: The extended q-Hahn class and the q-Askey scheme
Abstract: We will describe a class of q-orthogonal polynomial sequences that contains the q-Hahn class and all the families of q-orthogonal sequences in the q-Askey scheme, including the Askey-Wilson and the q-Racah polynomials, and many other sequences that are not listed in the q-Askey scheme. We will present explicit formulas for the recurrence coefficients of all the elements in the extended q-Hahn class using four parameters and show  how each family of sequences in the q-Askey scheme is obtained by direct substitution of the parameters with  appropriate values, without taking limits. In addition, we will discuss a general basic hypergeometric representation, in terms of the same four parameters, that yields the representation for each family in the q-Askey scheme by substitution of the parameters with appropriate values. 
The extended q-Hahn class was obtained using a matrix approach to study orthogonal polynomials and is closed under certain involutions that allow us to avoid taking limits to give particular values to the parameters in the general formulas.