Ocene grešaka kvadraturnih formula Gausovog tipa za analitičke funkcije
2013
Authors
Pejčev, AleksandarContributors
Spalević, MiodragMilovanović, Gradimir V.
Stanić, Marija
Bojović, Dejan
Pranić, Miroslav S.
Doctoral thesis (Published version)
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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.
Keywords:
numerička integracija / Gausove kvadraturne formuleSource:
2013Publisher:
- Univerzitet u Kragujevcu, Prirodno-matematički fakultet
URI
http://eteze.kg.ac.rs/application/showtheses?thesesId=66https://nardus.mpn.gov.rs/handle/123456789/3560
https://fedorakg.kg.ac.rs/fedora/get/o:125/bdef:Content/download
https://machinery.mas.bg.ac.rs/handle/123456789/17
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Mašinski fakultetTY - THES AU - Pejčev, Aleksandar PY - 2013 UR - http://eteze.kg.ac.rs/application/showtheses?thesesId=66 UR - https://nardus.mpn.gov.rs/handle/123456789/3560 UR - https://fedorakg.kg.ac.rs/fedora/get/o:125/bdef:Content/download UR - https://machinery.mas.bg.ac.rs/handle/123456789/17 AB - 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. PB - Univerzitet u Kragujevcu, Prirodno-matematički fakultet T1 - Ocene grešaka kvadraturnih formula Gausovog tipa za analitičke funkcije UR - https://hdl.handle.net/21.15107/rcub_nardus_3560 ER -
@phdthesis{ author = "Pejčev, Aleksandar", year = "2013", abstract = "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.", publisher = "Univerzitet u Kragujevcu, Prirodno-matematički fakultet", title = "Ocene grešaka kvadraturnih formula Gausovog tipa za analitičke funkcije", url = "https://hdl.handle.net/21.15107/rcub_nardus_3560" }
Pejčev, A.. (2013). Ocene grešaka kvadraturnih formula Gausovog tipa za analitičke funkcije. Univerzitet u Kragujevcu, Prirodno-matematički fakultet.. https://hdl.handle.net/21.15107/rcub_nardus_3560
Pejčev A. Ocene grešaka kvadraturnih formula Gausovog tipa za analitičke funkcije. 2013;. https://hdl.handle.net/21.15107/rcub_nardus_3560 .
Pejčev, Aleksandar, "Ocene grešaka kvadraturnih formula Gausovog tipa za analitičke funkcije" (2013), https://hdl.handle.net/21.15107/rcub_nardus_3560 .