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undergraduate thesis
Interpolacija polinomom
2021. urn:nbn:hr:179:667563
Šerkinić, Mate
University of Split
Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture
Department of Mathematics and Physics

Cite this document

Šerkinić, M. (2021). Interpolacija polinomom (Undergraduate thesis). Split: University of Split, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture. Retrieved from https://urn.nsk.hr/urn:nbn:hr:179:667563

Šerkinić, Mate. "Interpolacija polinomom." Undergraduate thesis, University of Split, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, 2021. https://urn.nsk.hr/urn:nbn:hr:179:667563

Šerkinić, Mate. "Interpolacija polinomom." Undergraduate thesis, University of Split, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, 2021. https://urn.nsk.hr/urn:nbn:hr:179:667563

Šerkinić, M. (2021). 'Interpolacija polinomom', Undergraduate thesis, University of Split, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, accessed 15 November 2024, https://urn.nsk.hr/urn:nbn:hr:179:667563

Šerkinić M. Interpolacija polinomom [Undergraduate thesis]. Split: University of Split, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture; 2021 [cited 2024 November 15] Available at: https://urn.nsk.hr/urn:nbn:hr:179:667563

M. Šerkinić, "Interpolacija polinomom", Undergraduate thesis, University of Split, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, Split, 2021. Available at: https://urn.nsk.hr/urn:nbn:hr:179:667563

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Metadata
TitleInterpolacija polinomom
Title (english)Polynomial interpolation
AuthorMate Šerkinić
MentorIvančica Mirošević (mentor)
GranterUniversity of Split
Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture
(Department of Mathematics and Physics)
Split
Defense date and country2021-09-21, Croatia
Scientific / art field,
discipline and subdiscipline		TECHNICAL SCIENCES
Computing
Abstract
Interpolacija čvorova polinomom je postupak određivanja polinoma najnižeg mogućeg stupnja čiji graf prolazi zadanim čvorovima. U ovom radu su objašnjena tri načina računanja interpolacijskog polinoma: s pomoću Lagrangeovog oblika interpolacijskog polinoma, s pomoću Newtonovog oblika interpolacijskog polinoma i direktno, Gaussovom metodom eliminacije na Vandermondovoj matrici. Uz objašnjene metode, navedena su i dva jako bitna teorema za interpolaciju, zajedno s njihovim dokazima. To su teorem koji tvrdi da je interpolacijski polinom jedinstven i teorem koji nam daje formulu za računanje ocjene pogreške pri aproksimaciji funkcije interpolacijskim polinomom. Nedostatak interpolacije polinomom je u tome što je računanje takvog polinoma, i njegovo izvrednjavanje, za veliki broj čvorova vremenski jako zahtjevno. Zbog toga se ovakva interpolacija u praksi rijetko koristi ako je broj čvorova koje treba interpolirati velik. U takvim slučajevima bolje rješenje je interpolacija po dijelovima polinomima, tzv. splajnovima. Također, kod interpolacije nekih funkcija može se javiti Rungeov fenomen, kada niz interpolacijskih polinoma ne konvergira (po točkama) prema funkciji koju aproksimiramo kad se broj čvorova povećava.
Abstract (english)
Polynomial interpolation is the process of determining the polynomial of the lowest possible degree whose graph passes through given nodes. In this final work, three ways of computing an interpolation polynomial are explained: using the Lagrange polynomial interpolation form, using the Newton polynomial interpolation form and directly, by Gaussian elimination method on the Vandermond matrix. In addition to the methods explained, two important interpolation theorems are listed, along with their proofs. These are the theorem that claims that the interpolation polynomial is unique and the theorem that gives us a formula for calculating the error estimate when approximating a function by an interpolation polynomial. The disadvantage of polynomial interpolation is that the calculation of such a polynomial, and its evaluation, is very time consuming for a large number of nodes. Therefore, such interpolation is rarely used in practice if the number of nodes to be interpolated is large. In such cases, a better solution is polynomial interpolation by parts, the so-called splines. Also, when interpolating some functions, the Runge phenomenon can occur, when a sequence of interpolation polynomials does not converge (pointwise) to a function that we approximate when the number of nodes increases.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:179:667563
Study programmeTitle: Computing
Study programme type: professional
Study level: undergraduate
Academic / professional title: stručni/a prvostupnik/ prvostupnica inženjer/inženjerka računarstva (stručni/a prvostupnik/ prvostupnica inženjer/inženjerka računarstva)
Type of resourceText
File originBorn digital
Access conditionsAccess restricted to students and staff of home institution
Terms of useLicence In copyright icon
Created on2021-12-09 14:15:15