Title
Ocene grešaka kvadraturnih formula Gausovog tipa za analitičke funkcije
Creator
Pejčev, Aleksandar, 1985-
Copyright date
2012
Object Links
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Autorstvo 3.0 Srbija (CC BY 3.0)
License description
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Language
Serbian
Cobiss-ID
Theses Type
Doktorska disertacija
Other responsibilities
mentor
Spalević, Miodrag M., 1961-
član komisije
Milovanović, Gradimir V., 1948-
član komisije
Stanić, Marija, 1975-
član komisije
Bojović, Dejan, 1968-
član komisije
Pranić, Miroslav
Academic Expertise
Prirodno-matematičke nauke
University
Univerzitet u Kragujevcu
Faculty
Prirodno-matematički fakultet
Format
PDF/A (listova)
description
datum odbrane 23.03.2013.
Abstract (en)
The field of research in this dissertation is concerned with numerical integration,i.e. with the derivation of error bounds for Gauss-type quadratures
and their generalizations when we use them to approximate integrals of functions
which are analytic inside an elliptical contour Eρ with foci at ∓1 and
sum of semi-axes ρ > 1. Special attention is given to Gauss-type quadratures
with the special kind of weight functions - weight functions of Bernstein–Szeg˝o
type. Three kinds of error bounds are considered in the dissertation, which
means analysis of kernels of quadratures, i.e. determination of the location
of the extremal point on Eρ at which the modulus of the kernels attains its
maximum, calculation of the contour integral of the modulus of the kernel,
and, also, series expansion of the kernel. Beyond standard, corresponding
quadratures for calculation of Fourier expansion coefficients of an analytic
function are also analysed in this dissertation.
Authors Key words
numerička integracija, Gausove kvadraturne formule
Abstract (en)
The field of research in this dissertation is concerned with numerical integration,i.e. with the derivation of error bounds for Gauss-type quadratures
and their generalizations when we use them to approximate integrals of functions
which are analytic inside an elliptical contour Eρ with foci at ∓1 and
sum of semi-axes ρ > 1. Special attention is given to Gauss-type quadratures
with the special kind of weight functions - weight functions of Bernstein–Szeg˝o
type. Three kinds of error bounds are considered in the dissertation, which
means analysis of kernels of quadratures, i.e. determination of the location
of the extremal point on Eρ at which the modulus of the kernels attains its
maximum, calculation of the contour integral of the modulus of the kernel,
and, also, series expansion of the kernel. Beyond standard, corresponding
quadratures for calculation of Fourier expansion coefficients of an analytic
function are also analysed in this dissertation.
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