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master's thesis
Jacobijeva metoda za simetrični problem svojstvenih vrijednosti
Zagreb: University of Zagreb, Faculty of Science, 2022. urn:nbn:hr:217:932021
Marinović, Toni
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Marinović, T. (2022). Jacobijeva metoda za simetrični problem svojstvenih vrijednosti (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:932021

Marinović, Toni. "Jacobijeva metoda za simetrični problem svojstvenih vrijednosti." Master's thesis, University of Zagreb, Faculty of Science, 2022. https://urn.nsk.hr/urn:nbn:hr:217:932021

Marinović, Toni. "Jacobijeva metoda za simetrični problem svojstvenih vrijednosti." Master's thesis, University of Zagreb, Faculty of Science, 2022. https://urn.nsk.hr/urn:nbn:hr:217:932021

Marinović, T. (2022). 'Jacobijeva metoda za simetrični problem svojstvenih vrijednosti', Master's thesis, University of Zagreb, Faculty of Science, accessed 16 May 2024, https://urn.nsk.hr/urn:nbn:hr:217:932021

Marinović T. Jacobijeva metoda za simetrični problem svojstvenih vrijednosti [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2022 [cited 2024 May 16] Available at: https://urn.nsk.hr/urn:nbn:hr:217:932021

T. Marinović, "Jacobijeva metoda za simetrični problem svojstvenih vrijednosti", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2022. Available at: https://urn.nsk.hr/urn:nbn:hr:217:932021

Metadata
TitleJacobijeva metoda za simetrični problem svojstvenih vrijednosti
Title (english)Jacobi method for the symmetric problem of eigenvalues
AuthorToni Marinović
MentorNela Bosner (mentor)
Committee memberNela Bosner (predsjednik povjerenstva)
Committee memberNenad Antonić (član povjerenstva)
Committee memberIgor Ciganović (član povjerenstva)
Committee memberMaja Resman (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2022-03-03, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom diplomskom radu smo opisali ideju iterativne Jacobijeve metode za računanje svojstvenih vrijednosti pune simetrične matrice. U prvom poglavlju smo naveli osnovne tvrdnje o simetričnim matricama i svojstvenim vrijednostima. Drugo poglavlje započinjemo izvodom same metode i dokazujemo njenu konvergenciju. U nastavku smo obradili nekoliko različitih varijanti te ih ilustrirali algoritmima. Nakon toga smo naveli rezultate o točnosti izračunatih svojstvenih vrijednosti i vektora,a na samom kraju smo naveli rezultate dobivene testiranjem algoritama, programima izradenim u MATLAB-u, na konkretnim primjerima iz kojih je vidljiva njihova točnost.
Abstract (english)
In this thesis we have described the idea of iterative Jacobi method for computing eigenvalues of a real symmetric matrix. In the first chapter we have named basic claims about symmetric matrices and eigenvalues. We start the second chapter with derivation of the method and we prove its convergence. We continue by describing several different variants and illustrate them with algorithms. After that, we proceed by presenting results on the accuracy of the calculated eigenvalues and eigenvectors, and at the very end we present the results obtained by testing the algorithms, by programs made using MATLAB, on specific examples that demonstrate their accuracy.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:932021
Study programmeTitle: Applied Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2022-03-28 12:05:16