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Pejčev, Aleksandar, 1985-

Ocene grešaka kvadraturnih formula Gausovog tipa za analitičke funkcije

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Academic metadata

Doktorska disertacija

Prirodno-matematičke nauke

Univerzitet u Kragujevcu

Prirodno-matematički fakultet

Other Theses Metadata

PDF/A (listova)

datum odbrane 23.03.2013.

Spalević, Miodrag M., 1961- (mentor)

Milovanović, Gradimir V., 1948- (član komisije)

Stanić, Marija, 1975- (član komisije)

Bojović, Dejan, 1968- (član komisije)

Pranić, Miroslav (član komisije)

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.

numerička integracija, Gausove kvadraturne formule

Serbian

518517653

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.