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undergraduate thesis
Chebyshevljeva aproksimacija
Rijeka: University of Rijeka, Faculty of Engineering, 2020. urn:nbn:hr:190:558745
Repušić, Luka
University of Rijeka
Faculty of Engineering
Department of Mathematics, Physics, and Foreign Languages
Section of Applied Mathematics

Institutional repository: Repository of the University of Rijeka, Faculty of Engineering

Cite this document

Repušić, L. (2020). Chebyshevljeva aproksimacija (Undergraduate thesis). Rijeka: University of Rijeka, Faculty of Engineering. Retrieved from https://urn.nsk.hr/urn:nbn:hr:190:558745

Repušić, Luka. "Chebyshevljeva aproksimacija." Undergraduate thesis, University of Rijeka, Faculty of Engineering, 2020. https://urn.nsk.hr/urn:nbn:hr:190:558745

Repušić, Luka. "Chebyshevljeva aproksimacija." Undergraduate thesis, University of Rijeka, Faculty of Engineering, 2020. https://urn.nsk.hr/urn:nbn:hr:190:558745

Repušić, L. (2020). 'Chebyshevljeva aproksimacija', Undergraduate thesis, University of Rijeka, Faculty of Engineering, accessed 27 July 2024, https://urn.nsk.hr/urn:nbn:hr:190:558745

Repušić L. Chebyshevljeva aproksimacija [Undergraduate thesis]. Rijeka: University of Rijeka, Faculty of Engineering; 2020 [cited 2024 July 27] Available at: https://urn.nsk.hr/urn:nbn:hr:190:558745

L. Repušić, "Chebyshevljeva aproksimacija", Undergraduate thesis, University of Rijeka, Faculty of Engineering, Rijeka, 2020. Available at: https://urn.nsk.hr/urn:nbn:hr:190:558745

Metadata
TitleChebyshevljeva aproksimacija
Title (english)Chebyshev approximation
AuthorLuka Repušić
MentorIvan Dražić (mentor)
MentorViktor Sučić (komentor)
Committee memberViktor Sučić (predsjednik povjerenstva)
Committee memberIvan Dražić (član povjerenstva)
GranterUniversity of Rijeka
Faculty of Engineering
(Department of Mathematics, Physics, and Foreign Languages)
(Section of Applied Mathematics)
Rijeka
Defense date and country2020-05-19, Croatia
Scientific / art field,
discipline and subdiscipline		TECHNICAL SCIENCES
Electrical Engineering
Abstract
Teorija aproksimacija govori o što boljem prikazu, aproksimaciji jedne funkcije nekom drugom, jednostavnijom funkcijom. U nekim slučajevima možemo ocjeniti grešku aproksimacije, ali u najčešćim slučajevima ocjenu greške nemoguće je odrediti zbog manjka informacija originalne funkcije. Za još lakše rješavanje funkcija koristimo svojstvo okomitosti, tj. ortogonalnosti, te ortogonalne polinome koji, osim svojstva ortogonalnosti, sadrže i određena svojstva polinoma. Kao vrsta ortogonalnih polinoma, Chebyshevljevi polinomi su nam, u ovom slucaju, od znatne važnosti budući da pomoću njih možemo vrlo dobro odrediti polinome minimalne pogreške u procesu zvanom Chebyshevljeva aproksimacija. Jedna od mogucih primjena također je i u području digitalnih filtera, pa tako postoji i Chebyshevljev filter koji je naziv dobio po Chebyshevljevim polinomima budući da iz njih proizlaze njegove matematičke karakteristike.
Abstract (english)
Approximation theory is concerned about how best to show, approximate, one function with another, much simpler function. In some cases we can rate the approximation error but in most cases the rate of error is impossible to determine because of lack of information from the original function. For even more simplicity during function solving we use the property of orthogonality and orthogonal polynomials which, apart from their properties of orthogonality, also have some properties of polynomials. As a part of orthogonal plyonomials, Chebyshev polynomials are, in this case, of utmost importance since we can obtain optimal polynomials using a process called Chebyshev approximation. Another possible application is also in the field of digital filters, there we can find Chebyshev filter whose name derives from Chebyshev polynomials since they are the origin of its mathematical characteristics.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:190:558745
Study programmeTitle: Undergraduate University Study of Electrical Engineering
Study programme type: university
Study level: undergraduate
Academic / professional title: sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka elektrotehnike (sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka elektrotehnike)
Type of resourceText
File originBorn digital
Access conditionsAccess restricted to students and staff of home institution
Terms of useLicence In copyright icon
Created on2020-12-14 08:35:17