Neke modifikacije klasičnih mera, odgovarajući ortogonalni polinomi i kvadrature Gausovog tipa
Some modifications of classical measures, corresponding orthogonal polynomials and quadratures of Gaussian type
Докторанд
Vasović, NevenaМентор
Milovanović, Gradimir V.Чланови комисије
Stanić, MarijaTomović, Tatjana
Matejić, Marjan
Метаподаци
Приказ свих података о дисертацијиСажетак
Sažetak:
Predmet ove disertacije jesu polinomi realne promenljive ortogonalni u odnosu
na polinomske modifikacije Čebiševljevih mera prve i druge vrste, njihova simboliqka izraqunavanja i diferencne osobine. Pored ovoga, predmet disertacije
jeste i efikasan numerički algoritam za konstrukciju parametara generalizovanih
Gaus-Risovih kvadraturnih formula i numerička konstrukcija odgovarajuih klasa
ortogonalnih polinoma.
Za polinome ortogonalne u odnosu na modifikovane Čebiševljeve mere prve i
druge vrste određeni su koeficijenti tročlane rekurentne relacije u simboličkom
obliku i ispitivane su njihove diferencno-diferencijabilne osobine. Pored ovoga,
pretpostavljajući logaritamski potencijal data je elektrostatiqka interpretacija
nula polinoma ortogonalnih u odnosu na modifikovanu Čebiševljevu meru prve vrste.
Abstract:
In this thesis we consider the polynomials of real variable orthogonal with respect to
the polynomial modifications of the Chebyshev measures of the first and second kind,
its symbolic calculations and difference properties. In addition, the subject of this dissertation is an efficient numerical algorithm for the construction of parameters of the
generalized Gauss-Rys quadrature formulas and numerical construction of the corresponding orthogonal polynomials.
For polynomials orthogonal with respect to the modified Chebyshev measures of the
first and second kind, the coefficients of the three-term recurrence relation are obtained
in their symbolic form and also the difference properties are examined. Furthermore,
assuming a logarithmic potential, we gave an electrostatic interpretation of the zeros of
the polynomials orthogonal with respect to the modified Chebyshev measure of the first
kind.
In a recent paper by Milovanovi´c [48], an efficient numerical algorithm fo...r the construction of Guass-Rys quadratures was given. In this study, the so-called generalized
Gauss-Rys quadrature formulas with respect to the product of the exponential function
exp (−xt2
) and the ultraspherical Gegenbauer weight function are studied, with a special
attention to the important Chebyshev cases.
All obtained results have been checked in the software Mathematica with intensive
use of the package OrthogonalPolynomials.