Paralelni algoritmi za QR faktorizaciju

master's thesis

• Author: Vedran Rukavina
• Mentor: Nela Bosner (mentor)
• Committee member: Nela Bosner (predsjednik povjerenstva)
• Committee member: Ana Prlić (član povjerenstva)
• Committee member: Snježana Lubura Strunjak (član povjerenstva)
• Committee member: Miljenko Marušić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2019-09-24, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom radu opisujemo serijske i paralelne algoritme za računanje QR faktorizacije. Opisujemo serijski algoritam za računanje QR faktorizaciju pomoću klasičnog i modificiranog Gram-Schmidtovog postupka te serijski algoritam koji koristi Householderove reflektore za računanje već spomenute faktorizacije. Opisujemo paralelne algoritme za računanje QR faktorizacije kao što su TSQR, CAQR i HRCAQR koja je ograničena varijanta CAQR. Neke od algoritama smo implementirali koristeći C programski jezik, a za paralelni algoritam smo koristili C s CUDA sučeljem. Na kraju rada su pokazani rezultati implementiranih algoritama uspoređeni s MATLAB - ovom implementacijom QR algoritama. Cijeli rad smo zaključili s diskusijom o dobivenim rezultatima.

Abstract (english)

In this paper, we describe serial and parallel algorithms for computing QR factorization. We describe a serial algorithm for computing QR factorization using the classical and modified Gram-Schmidt methods and a serial algorithm that uses Householder reflectors to calculate the factorization that we have already mentioned. We describe parallel algorithms for computing QR factorization such as TSQR, CAQR, and HRCAQR which is a restricted variant of CAQR. Some of the algorithms were implemented using the C programming language, and for the parallel algorithm, we used C with the CUDA interface. At the end of the paper, the results of the implemented algorithms are shown compared to MATLABs implementation of QR algorithms. We concluded the whole paper with a discussion of the obtained results.

• Keywords: QR faktorizacija; Gram-Schmidtov postupak; Householderovi reflektori; MATLAB
• Keywords (english): QR factorization; Gram-Schmidt methods; Householder reflectors; MATLAB
• Language: croatian
• URN:NBN: urn:nbn:hr:217:224975
• 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: 2020-02-24 13:34:02