Metode za određivanje QR dekompozicije

Per, Valentina

undergraduate thesis

Metode za određivanje QR dekompozicije

Per, Valentina (2018)

Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Applied Mathematics
Applied Mathematics Research Group

Cite this document

APA 6th Edition

Per, V. (2018). Metode za određivanje QR dekompozicije (Undergraduate thesis). Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:995552

MLA 8th Edition

Per, Valentina. "Metode za određivanje QR dekompozicije." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2018. https://urn.nsk.hr/urn:nbn:hr:126:995552

Chicago 17th Edition

Harvard

Per, V. (2018). 'Metode za određivanje QR dekompozicije', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 14 July 2020, https://urn.nsk.hr/urn:nbn:hr:126:995552

Vancouver

Per V. Metode za određivanje QR dekompozicije [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2018 [cited 2020 July 14] Available at: https://urn.nsk.hr/urn:nbn:hr:126:995552

IEEE

V. Per, "Metode za određivanje QR dekompozicije", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2018. Available at: https://urn.nsk.hr/urn:nbn:hr:126:995552

Cite this item: https://urn.nsk.hr/urn:nbn:hr:126:995552

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Metadata

Title	Metode za određivanje QR dekompozicije
Title (english)	Methods for determing QR decomposition
Author	Valentina Per
Mentor	Darija Marković (mentor)
Granter	Josip Juraj Strossmayer University of Osijek Department of Mathematics (Chair of Applied Mathematics) (Applied Mathematics Research Group) Osijek
Defense date and country	2018-09-20, Croatia
Scientific / art field, discipline and subdiscipline	NATURAL SCIENCES Mathematics Algebra
Abstract	U ovom radu najprije ćemo objasnit što je to QR dekompozicija matrice. Nakon toga ćemo navesti tri metode uz pomoću kojih možemo odrediti QR dekompoziciju dane matrice. Kao prvu od metoda za određivanje QR dekompozicije pojasnit ćemo Gram–Schmidtov postupak ortogonalizacije. Navest ćemo osnovne definicije i teoreme vezane za ortogonalnost te pojasniti sam Gram–Schmidtov postupak. Opisanu metodu ilustrirat ćemo primjerom. U drugom poglavlju pojasnit ćemo QR dekompoziciju pomoću Householderovih transformacija. Definirat ćemo Householderove matrice i Householderov vektor. Opisat ćemo kako odredujemo QR dekompoziciju dane matrice te metodu ilustrirati primjerom. U posljednjem poglavlju pojasnit ćemo kako možemo odrediti QR dekompoziciju pomoću Givensovih rotacija. Uvest ćemo pojam matrica rotacija te navesti neka njihova osnovna svojstva. Zatim ćemo pojasniti Givensove rotacije te kako uz pomoć njih odrđujemo QR dekompoziciju. Također ćemo kao i u prethodnim poglavljima opisanu metodu ilustrirati primjerom.
Abstract (english)	In this paper we will first explain what a QR decomposition of the matrix is. After that, we will name three methods which can help us determine the QR decomposition of any given matrix. First method to be explained will be the Gram-Schmidt orthogonalization process. We will list the main definitions and theorems significant for orthogonalization and the Gram-Schmidt process itself will be explained. Described method we will apply on a given example. In second chapter we will clarify QR decomposition using Householder transformations. Householder matrixes and Householder vector will be define. We will clarify how to determine QR decomposition of a given matrix and apply it on an example. In last chapter we will explain how to determine QR decomposition using Givens rotations. We will define the term of matrix rotation and name some basic properties. Then, we will clarify Givens rotations and how to use them to determine QR decomposition. Also, we will explain the procedure using an example.
Keywords
Keywords (english)
Language	croatian
URN:NBN	urn:nbn:hr:126:995552
Study programme	Title: University undergraduate study programme in mathematics Study programme type: university Study level: undergraduate Academic / professional title: sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike (sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike)
Type of resource	Text
File origin	Born digital
Access conditions	Open access
Terms of use
Created on	2018-10-18 09:17:52