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undergraduate thesis
Gaussove kvadraturne formule
Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2020. urn:nbn:hr:126:277926
Cvenić, Doris
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Pure Mathematics and Mathematics Teaching
Algebra, Analysis and Number Theory Research Group

Institutional repository: Repository of School of Applied Mathematics and Informatics

Cite this document

Cvenić, D. (2020). Gaussove kvadraturne formule (Undergraduate thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:277926

Cvenić, Doris. "Gaussove kvadraturne formule." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2020. https://urn.nsk.hr/urn:nbn:hr:126:277926

Cvenić, Doris. "Gaussove kvadraturne formule." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2020. https://urn.nsk.hr/urn:nbn:hr:126:277926

Cvenić, D. (2020). 'Gaussove kvadraturne formule', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 03 January 2025, https://urn.nsk.hr/urn:nbn:hr:126:277926

Cvenić D. Gaussove kvadraturne formule [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2020 [cited 2025 January 03] Available at: https://urn.nsk.hr/urn:nbn:hr:126:277926

D. Cvenić, "Gaussove kvadraturne formule", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2020. Available at: https://urn.nsk.hr/urn:nbn:hr:126:277926

Metadata
TitleGaussove kvadraturne formule
Title (english)Gauss Quadrature Formulae
AuthorDoris Cvenić
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 country2020-09-30, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Numerical Mathematics
Abstract
U ovom završnom radu upoznat ćemo se s pojmom interpolacije funkcije polinomom te dokazati egzistenciju i jedinstvenost Hermiteovog interpolacijskog polinoma. Definirat ćemo Gaussove kvadraturne formule, te pokazati kako se one mogu dobiti integracijom Hermiteovog interpolacijskog polinoma. Detaljno ćemo obraditi specijalne slučajeve Gaussovih formula, Gauss-Legendreove formule te ćemo iskazati i dokazati tvrdnje koje pokazuju svojstva Legendreovih polinoma. Pokazat ćemo kako odrediti točke integracije i težinske koeficijente, te pronaći ocjene pogrešaka za te formule. Na kraju rada ćemo navesti neke od ostalih specijalnih slučajeva Gaussovih formula: Gauss-Čebiševljeve formule prve i druge vrste, Gauss-Laguerreove i Gauss-Hermiteove kvadraturne formule, te odgovarajuće primjere.
Abstract (english)
In this final paper, we will explain polynomial interpolation of a function, prove the existence and uniqueness of Hermite polynomials. We will define the Gaussian quadrature formulae, and show how it is obtained by integrating the Hermite interpolation polynomial. We will consider a special case of the Gaussian formulae, the GaussLegendre formulae, and we will state and prove statements that show the properties of Legendre polynomials. We will show how to determine integration points and weights, and find the error estimates. At the end of the paper, we will list some of the other special cases of the Gaussian formulae: Gauss-Chebyshev formulae of the first and of the second kind, Gauss-Laguerre and Gauss-Hermite quadrature formulae, and corresponding examples.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:277926
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 on2020-11-02 06:58:08