Одељење за математику, 12. децембар 2014.

Наредни састанак Семинара биће одржан у петак, 12. децембра 2014. у сали 301ф Математичког института САНУ са почетком у 14 часова.

Предавач:  Марија Станић, ПМФ Крагујевац

Наслов предавања: MULTIPLE ORTHOGONALITY AND APPLICATIONS IN NUMERICAL INTEGRATION

Садржај: Motivated by a problem that arise in the evaluation of computer graphics illumination models Carlos Borges in [Numer. Math. 67, 1994, str. 271--288] examined the more abstract problem of numerically evaluating of a set of r definite integrals taken with respect to distinct weight functions, but related to a common integrand and interval of integration. It turns out that such set of quadrature rules are closely related to the so-called type II multiple orthogonal polynomials.

In this lecture a brief survey of multiple orthogonal polynomials, defined using orthogonality conditions spread out over r>1 different measures, are given. Such polynomials satisfy a linear recurrence relation of order r+1, which is a generalization of the well known three-term recurrence relation for ordinary orthogonal polynomials (the case r=1).

Some applications of such orthogonal systems to numerical integration are given. Also, methods for the numerical construction of multiple orthogonal polynomials, as well as the corresponding optimal set of quadrature rules, based on the discretized Stieltjes-Gautschi procedure are presented.


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