undergraduate thesis
Error estimates of Newton-Cotes and Gauss-Chebyshev quadrature formulae using the Grüss inequality

Toni Milas (2015)
Sveučilište Josipa Jurja Strossmayera u Osijeku
Odjel za matematiku
Zavod za teorijsku matematiku
Katedra za algebru i matematičku analizu
Metadata
TitleOcjene pogrešaka Newton-Cotesovih i Gauss-Čebiševljevih kvadraturnih formula pomoću Grüssove nejednakosti
AuthorToni Milas
Mentor(s)Mihaela Ribičić Penava (thesis advisor)
Abstract
U ovom radu ukratko ćemo se upoznati s Newton-Cotesovim formulama i Gauss-Čebiševljevim kvadraturnim formulama prve vrste, koje su od iznimne važnosti u području numeričke integracije. Izvest ćemo općenitu zatvorenu Newton-Cotesovu formulu n-tog reda te dati standardnu ocjenu pogreške formule. Detaljnije ćemo prikazati teoriju Gaussovih kvadraturnih formula i standardnu ocjenu pogreške te kao specijalan slučaj prikazati Gauss-Čebiševljevu formulu prve vrste. U drugom dijelu rada iskazat i dokazat ćemo Grüssovu nejednakost te druge nejednakosti koje će nam biti od velike važnosti u prikazu dodatnih ocjena formula obradenih u radu. U zadnjem dijelu rada naglasak se stavlja na neke nedavno dokazane ocjene pogreške prethodno spomenutih pravila. Ocjene iz zadnjeg poglavlja utemeljene su prvenstveno na Grüssovoj nejednakosti.
Keywordsnumerical integration Newton-Cotes formulae Gaussian quadrature formulae Grüss inequality error estimates
Parallel title (English)Error estimates of Newton-Cotes and Gauss-Chebyshev quadrature formulae using the Grüss inequality
GranterSveučilište Josipa Jurja Strossmayera u Osijeku
Odjel za matematiku
Lower level organizational unitsZavod za teorijsku matematiku
Katedra za algebru i matematičku analizu
PlaceOsijek
StateCroatia
Scientific field, discipline, subdisciplineNATURAL SCIENCES
Mathematics
Algebra
Study programme typeuniversity
Study levelundergraduate
Study programmeUniversity undergraduate study programme in mathematics
Academic title abbreviationuniv.bacc.math.
Genreundergraduate thesis
Language Croatian
Defense date2015-09-30
Parallel abstract (English)
In this paper we will be shortly introduced to Newton-Cotes formulae and Gauss-Chebyshev quadrature formulae of the first kind, which are extremely important in the eld of numerical integration. We will derive the general closed Newton-Cotes formula of order n and provide the standard error estimate of the formula. The theory of Gaussian quadrature formulae and the error estimate will be given in great detail and the Gauss-Chebyshev formula of the first kind will be given as a special case. In the second part of the paper, the Grüss inequality will be formulated and proven, along with other inequalities which are important for proving some estimates of the previously mentioned formulae. The last part of the paper accentuates some newly proven error estimates of the formulae. The error estimates seen in the last part of the paper are primarily based on the Grüss inequality.
Parallel keywords (Croatian)numerička integracija Newton-Cotesove formule Gaussove kvadraturne formule Grüssova nejednakost ocjene pogreške aproksimacije
Resource typetext
Access conditionOpen access
Terms of usehttp://rightsstatements.org/vocab/InC/1.0/
URN:NBNhttps://urn.nsk.hr/urn:nbn:hr:126:489241
CommitterMirna Šušak Lukačević