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undergraduate thesis
Ocjene pogrešaka Newton-Cotesovih i Gauss-Čebiševljevih kvadraturnih formula pomoću Grüssove nejednakosti
2015. urn:nbn:hr:126:489241
Milas, Toni
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Pure Mathematics and Mathematics Teaching
Algebra, Analysis and Number Theory Research Group

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Milas, T. (2015). Ocjene pogrešaka Newton-Cotesovih i Gauss-Čebiševljevih kvadraturnih formula pomoću Grüssove nejednakosti (Undergraduate thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:489241

Milas, Toni. "Ocjene pogrešaka Newton-Cotesovih i Gauss-Čebiševljevih kvadraturnih formula pomoću Grüssove nejednakosti." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2015. https://urn.nsk.hr/urn:nbn:hr:126:489241

Milas, Toni. "Ocjene pogrešaka Newton-Cotesovih i Gauss-Čebiševljevih kvadraturnih formula pomoću Grüssove nejednakosti." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2015. https://urn.nsk.hr/urn:nbn:hr:126:489241

Milas, T. (2015). 'Ocjene pogrešaka Newton-Cotesovih i Gauss-Čebiševljevih kvadraturnih formula pomoću Grüssove nejednakosti', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 24 December 2024, https://urn.nsk.hr/urn:nbn:hr:126:489241

Milas T. Ocjene pogrešaka Newton-Cotesovih i Gauss-Čebiševljevih kvadraturnih formula pomoću Grüssove nejednakosti [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2015 [cited 2024 December 24] Available at: https://urn.nsk.hr/urn:nbn:hr:126:489241

T. Milas, "Ocjene pogrešaka Newton-Cotesovih i Gauss-Čebiševljevih kvadraturnih formula pomoću Grüssove nejednakosti", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2015. Available at: https://urn.nsk.hr/urn:nbn:hr:126:489241

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Metadata
TitleOcjene pogrešaka Newton-Cotesovih i Gauss-Čebiševljevih kvadraturnih formula pomoću Grüssove nejednakosti
Title (english)Error estimates of Newton-Cotes and Gauss-Chebyshev quadrature formulae using the Grüss inequality
AuthorToni Milas
MentorMihaela Ribičić Penava (mentor)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
(Chair of Pure Mathematics and Mathematics Teaching)
(Algebra, Analysis and Number Theory Research Group)
Osijek
Defense date and country2015-09-30, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Algebra
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.
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.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:489241
Study programmeTitle: University undergraduate study programme in mathematics
Study programme type: university
Study level: undergraduate
Academic / professional title: sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike (sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
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Created on2015-11-04 12:19:24