Live streamed at https://fc-up-pt.zoom.us/j/87114325217

Website of PGSFOPA https://www.mat.uc.pt/~pgsfop

Video of exhibition https://youtu.be/Kek6JCFvJ1A 

 

 

Date: July, 12th 2023

Venue: Department of Mathematics of Faculty of Sciences of University of Porto

Organized by Kenier Castillo (CMUC, DMUC), and Zélia da Rocha (CMUP, DM-FCUP)

 

11h – Welcome and coffee break 

Room FC1-0.07

 

11h30m – Kenier Castillo and Zélia da Rocha

CMUC - Department of Mathematics of University of Coimbra and

CMUP - Department of Mathematics of Faculty of Sciences of University of Porto

 

“Introduction to PGSFOPA”

Room FC1-0.07

 

Lunch

 

SEMINARS and EXHIBITION

FCUP Library – 2nd floor – FC1

 

14h30m - Semyon Yakubovich (on behalf of CMUP)

Department of Mathematics of Faculty of Sciences of University of Porto

 

14h45m - Claude Brezinski

University of Lille, France

“The birth of orthogonal polynomials”

 

In this talk, we present the first appearance of orthogonal polynomials in mathematics. The story begins with Lagrange who gave them but did not know they were orthogonal. He was followed by Legendre who was the first to discover them, and, almost simultaneously by Laplace. The three-term recurrence relation will be evoked.

 

15h30m – Pascal Maroni

CNRS - University of Pierre Marie Curie, France

“Quelques remarques au sujet de la décomposition quadratique des polynômes de Laguerre”

 

 

15h45m – Michela Redivo-Zaglia 

Department of Mathematics Tullio Levi-Civita, University of Padua, Italy

“Treatment of near-breakdown in the conjugate gradient algorithm”

 

The conjugate gradient algorithm for solving systems of linear equations with a symmetric positive definite matrix was obtained in 1952 by Magnus Rudolph Hestenes (1906-1991) and  Eduard Stiefel (1909-1978). It is a direct method since, for a system of dimension N, it converges in N iterations at most. When N is large, it is used as an iterative method.

The conjugate gradient algorithm makes use of two recurrence relations each of them depending on a rational coefficient changing at each step. It cannot suffer from a breakdown due to a division by zero in the computation of the coefficients of the recurrence relations.

However, the algorithm can suffer from a near-breakdown when the denominator of one of these coefficients (or when the coefficient itself) is close to zero, thus leading to rounding errors and non-convergence. First, we will give some examples showing that a near-breakdown really arises. Then, we will derive the recurrence relations for jumping over it. This is a joint work in progress with Claude Brezinski.

 

16h30 Visit to the bibliographic exhibition of Claude Brezinski, Michela Redivo-Zaglia and Pascal Maroni

Video available at https://youtu.be/Kek6JCFvJ1A 

 

17h Closing and Coffee break

 

Sponsors: CMUC, DMUC, CMUP, DM-FCUP, FCT