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master's thesis
Preprocessing Algorithm for the Generalized SVD on the Graphics Processing Units
Zagreb: University of Zagreb, Faculty of Science, 2016. urn:nbn:hr:217:008225
Flegar, Goran
University of Zagreb
Faculty of Science
Department of Mathematics

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Flegar, G. (2016). Preprocessing Algorithm for the Generalized SVD on the Graphics Processing Units (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:008225

Flegar, Goran. "Preprocessing Algorithm for the Generalized SVD on the Graphics Processing Units." Master's thesis, University of Zagreb, Faculty of Science, 2016. https://urn.nsk.hr/urn:nbn:hr:217:008225

Flegar, Goran. "Preprocessing Algorithm for the Generalized SVD on the Graphics Processing Units." Master's thesis, University of Zagreb, Faculty of Science, 2016. https://urn.nsk.hr/urn:nbn:hr:217:008225

Flegar, G. (2016). 'Preprocessing Algorithm for the Generalized SVD on the Graphics Processing Units', Master's thesis, University of Zagreb, Faculty of Science, accessed 19 April 2024, https://urn.nsk.hr/urn:nbn:hr:217:008225

Flegar G. Preprocessing Algorithm for the Generalized SVD on the Graphics Processing Units [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2016 [cited 2024 April 19] Available at: https://urn.nsk.hr/urn:nbn:hr:217:008225

G. Flegar, "Preprocessing Algorithm for the Generalized SVD on the Graphics Processing Units", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2016. Available at: https://urn.nsk.hr/urn:nbn:hr:217:008225

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Metadata
TitlePreprocessing Algorithm for the Generalized SVD on the Graphics Processing Units
AuthorGoran Flegar
MentorSanja Singer (mentor)
Committee memberSanja Singer (predsjednik povjerenstva)
Committee memberNela Bosner (član povjerenstva)
Committee memberZvonimir Bujanović (član povjerenstva)
Committee memberMarko Vrdoljak (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2016-07-01, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
In this thesis we study a preprocessing algorithm for the generalized SVD and its parallelization on the graphics processing unit. The preprocessing algorithm reduces a general matrix pair (A; B) to an upper triangular matrix pair (\(\tilde{A}, \tilde{B}\)) where B is nonsingular. After the preprocessing step a specialized algorithm, such as the implicit Kogbetliantz or the Hari–Zimmerman algorithm, which requires this structure of the matrix pair can be used to compute the generalized SVD. In the first chapter of the thesis we define the generalized SVD and describe the upper triangular decomposition resulting from the preprocessing step. Additionally, we describe the complete orthogonal decomposition which is used in the preprocessing step. The second chapter describes the challenges that arise when developing algorithms for the GPU and presents an efficient implementation of the preprocessing step. In the final chapter we test the algorithm on a variety of matrices of different sizes and compare the speed, rank detection, backward error and the effect on generalized singular values of our algorithm and LAPACK’s and MKL’s versions of xGGSVP.
Abstract (croatian)
U ovom radu proučavamo algoritam pretprocesiranja za generalizirani SVD i njegovu paralelizaciju na grafičkoj kartici. Algoritam pretprocesiranja reducira par proizvoljnih matrica (A; B) na gornje trokutasti par (\(\tilde{A}, \tilde{B}\)) pri čemu je $\tilde{B}$ regularna matrica. Nakon algoritma pretprocesiranja za računanje generaliziranog SVD-a mogu se iskoristiti specijalizirani algoritmi, kao sto je implicitni Kogbrliantzov ili implicitni Hari–Zimmermanov algoritam, koji zahtijevaju ovakvu strukturu para matrica. U prvom poglavlju rada definiramo generalizirani SVD i opisujemo gornje trokutastu faktorizaciju koja je rezultat pretprocesiranja. Dodatno, opisujemo potpunu ortogonalnu faktorizaciju korištenu u postupku pretprocesiranja. U drugom poglavlju opisuju se izazovi koji se pojavljuju pri razvoju algoritama za grafičke kartice te se daje efikasna implementacija algoritma pretprocesiranja. U zadnjem poglavlju testiramo razvijeni algoritam na matricama različitih veličina i uspoređujemo brzinu, detekciju ranga, povratnu grešku i utjecaj na generalizirane singularne vrijednosti našeg algoritma te LAPACK-ove i MKL-ove verzije procedure xGGS VP.
Keywords
Keywords (croatian)
Languageenglish
URN:NBNurn:nbn:hr:217:008225
Study programmeTitle: Computer Science and Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra računarstva i matematike (magistar/magistra računarstva i matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
RepositoryRepository of the Faculty of Science
Created on2019-01-22 10:16:09

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