Nove metode za računanje spektralne dekompozicije simetrične matrice reda 3 i 4

master's thesis

• Author: Marija Kranjčević
• Mentor: Vjeran Hari (mentor)
• Committee member: Vjeran Hari (predsjednik povjerenstva)
• Committee member: Tina Bosner (član povjerenstva)
• Committee member: Maja Starčević (član povjerenstva)
• Committee member: Dražen Adamović (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2015-07-10, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom radu prezentiramo novu metodu za spektralnu dekompoziciju simetričnih matrica reda 3 i 4, koja se bazira na algoritmu aheig (ArrowHEead EIGenvalues/eigenvectors) za spektralnu dekompoziciju streličastih matrica. U poglavlju 1 uvodimo osnovne pojmove i rezultate koje kasnije koristimo. Zatim detaljno opisujemo i analiziramo algoritam aheig (poglavlje 2), te ga kombiniramo s Jacobijevim rotacijama (poglavlje 3) kako bi dobili algoritam za spektralnu dekompoziciju simetričnih matrica reda 3 i 4 (poglavlje 4). Prilažemo Matlab kodove svih opisanih algoritama, te dajemo odgovaraju će primjere.

Abstract (english)

We present a new method for the spectral decomposition of symmetric matrices of order 3 and 4, which is based on the algorithm aheig (ArrowHEead EIGenvalues/eigenvectors) for the spectral decomposition of arrowhead matrices. In Chapter 1 we give some basic definitions and results. Then we describe and analyze the aheig algorithm (Chapter 2) and combine it with Jacobi rotations (Chapter 3) to get an algorithm for the spectral decomposition of symmetric matrices of order 3 and 4 (Chapter 4). We implement all the presented algorithms in Matlab and show some interesting examples.

• Keywords: spektralna dekompozicija; simetrične matrice; aheig algoritam; streličaste matrice; Jacobijeve rotacije; MATLAB
• Keywords (english): spectral decomposition; symmetric matrices; aheig algorithm; arrowhead matrices; Jacobi rotations; MATLAB
• Language: croatian
• URN:NBN: urn:nbn:hr:217:909396
• 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: 2019-02-20 09:54:07