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master's thesis
Homogene linearne rekurzije
Zagreb: University of Zagreb, Faculty of Science, 2022. urn:nbn:hr:217:498986
Karlović, Luka
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Karlović, L. (2022). Homogene linearne rekurzije (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:498986

Karlović, Luka. "Homogene linearne rekurzije." Master's thesis, University of Zagreb, Faculty of Science, 2022. https://urn.nsk.hr/urn:nbn:hr:217:498986

Karlović, Luka. "Homogene linearne rekurzije." Master's thesis, University of Zagreb, Faculty of Science, 2022. https://urn.nsk.hr/urn:nbn:hr:217:498986

Karlović, L. (2022). 'Homogene linearne rekurzije', Master's thesis, University of Zagreb, Faculty of Science, accessed 05 May 2024, https://urn.nsk.hr/urn:nbn:hr:217:498986

Karlović L. Homogene linearne rekurzije [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2022 [cited 2024 May 05] Available at: https://urn.nsk.hr/urn:nbn:hr:217:498986

L. Karlović, "Homogene linearne rekurzije", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2022. Available at: https://urn.nsk.hr/urn:nbn:hr:217:498986

Metadata
TitleHomogene linearne rekurzije
Title (english)Homogeneous linear recursions
AuthorLuka Karlović
MentorZrinka Franušić (mentor)
Committee memberAndrej Dujella (predsjednik povjerenstva)
Committee memberZrinka Franušić (član povjerenstva)
Committee memberMarko Tomislav Cvitaš (član povjerenstva)
Committee memberBoris Muha (član povjerenstva)
Committee memberŽeljko Skoko (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2022-07-21, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Kažemo da niz \( (a_n)_{n\geq0}\) zadovoljava linearnu homogenu rekurzivnu relaciju s konstantnim koeficijentima reda \(k\) ako vrijedi \(a_n=c_1a_{n-1}+c_2a_{n-2}+\dots +c_k a_{n-k}\), za sve \(n\geq k\), pri čemu su \(c_1, c_2, \dots, c_k\in\mathbb{C}\) konstante, a prvih \(k\) članova niza \(a_0, a_1, \dots, a_{k-1}\) su početni uvjeti. U radu je opisana metoda eksplicitnog određivanja općeg člana rekurzivno zadanog niza koja se koristi alatima iz linearne algebre kao što je račun svojstvenih vrijednosti i vektora matrice, te metoda koja koristi karakterističnu jednadžbu rekurzije. Nadalje, proučavale su se i takozvane modularne rekurzije, odnosno linearne homogene rekurzije modulo neki fiksni prirodni broj. Njihovo glavno svojstvo je periodičnost uz kojeg se veže problem određivanja perioda.
Abstract (english)
A sequence \( (a_n)_{n\geq0}\) is said to satisfy a linear homogeneous recurrence relation with constant coefficients if \(a_n=c_1a_{n-1}+c_2a_{n-2}+\dots +c_k a_{n-k}\), is true for all \(n\geq k\), where \(c_1, c_2, \dots, c_k\in\mathbb{C}\), and the first \(k\) terms \(a_0, a_1, \dots, a_{k-1}\) are called initial values. In this thesis a method using techniques from linear algebra, such as eigenvalues and eigenvectors of a matrix, is described and applied to determine the general term of sequences satisfying these types of recurrence relations. A method using the characteristic equation of such sequences is also described. Moreover, modular recurrences, which are linear homogeneous recurrences modulo a fixed positive integer, are analysed. Their main property is periodicity, alongside which comes the problem of determining the period.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:498986
Study programmeTitle: Mathematics and Physics Education; specializations in: Mathematics and Physics Education
Course: Mathematics and Physics Education
Study programme type: university
Study level: integrated undergraduate and graduate
Academic / professional title: magistar/magistra edukacije matematike i fizike (magistar/magistra edukacije matematike i fizike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2022-09-13 10:55:25