Jacobijeva metoda za simetrični problem svojstvenih vrijednosti

master's thesis

• Title (english): Jacobi method for the symmetric problem of eigenvalues
• Author: Toni Marinović
• Mentor: Nela Bosner (mentor)
• Committee member: Nela Bosner (predsjednik povjerenstva)
• Committee member: Nenad Antonić (član povjerenstva)
• Committee member: Igor Ciganović (član povjerenstva)
• Committee member: Maja Resman (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2022-03-03, 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: iterativna Jacobijeva metoda; puna simetrična matrica; konvergencija; MATLAB
• Keywords (english): iterative Jacobi method; reall symmetric matrix; convergence; MATLAB
• Language: croatian
• URN:NBN: urn:nbn:hr:217:932021
• Study programme: Title: Applied Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2022-03-28 12:05:16