prikaz prve stranice dokumenta Recompression of Hadamard products of tensors in Tucker format
  Download
PDF 1.2 MB
doctoral thesis
Recompression of Hadamard products of tensors in Tucker format
Zagreb: University of Zagreb, Faculty of Science, 2017. urn:nbn:hr:217:508763
Periša, Lana
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Periša, L. (2017). Recompression of Hadamard products of tensors in Tucker format (Doctoral thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:508763

Periša, Lana. "Recompression of Hadamard products of tensors in Tucker format." Doctoral thesis, University of Zagreb, Faculty of Science, 2017. https://urn.nsk.hr/urn:nbn:hr:217:508763

Periša, Lana. "Recompression of Hadamard products of tensors in Tucker format." Doctoral thesis, University of Zagreb, Faculty of Science, 2017. https://urn.nsk.hr/urn:nbn:hr:217:508763

Periša, L. (2017). 'Recompression of Hadamard products of tensors in Tucker format', Doctoral thesis, University of Zagreb, Faculty of Science, accessed 24 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:508763

Periša L. Recompression of Hadamard products of tensors in Tucker format [Doctoral thesis]. Zagreb: University of Zagreb, Faculty of Science; 2017 [cited 2024 December 24] Available at: https://urn.nsk.hr/urn:nbn:hr:217:508763

L. Periša, "Recompression of Hadamard products of tensors in Tucker format", Doctoral thesis, University of Zagreb, Faculty of Science, Zagreb, 2017. Available at: https://urn.nsk.hr/urn:nbn:hr:217:508763

Metadata
TitleRecompression of Hadamard products of tensors in Tucker format
Title (croatian)Rekompresija Hadamardovog produkta tenzora u Tuckerovom formatu
AuthorLana Periša
MentorIvan Slapničar (mentor)
MentorDaniel Kressner (komentor)
MBZ: 283256
Committee memberLuka Grubišić (predsjednik povjerenstva)
Committee memberZvonimir Bujanović (član povjerenstva)
Committee memberNinoslav Truhar (član povjerenstva)
Committee memberIvan Slapničar (član povjerenstva)
Committee memberDaniel Kressner (član povjerenstva)
MBZ: 283256
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2017-11-23, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Universal decimal classification
(UDC)		51 - Mathematics
Abstract
In the last decade low-rank tensors decompositions have been established as a new tool in scientific computing to address large-scale linear and multilinear algebra problems, which would be intractable by classical techniques. Since tensors can be given only as the solution of some algebraic equation, it is important to develop solvers working within the compressed storage scheme. That is what this thesis is concerned with, focusing on Tucker format, one of the most commonly used low-rank representation of tensors, and Hadamard product, which features prominently in tensor-based algorithms in scientific computing and data analysis. Fast algorithms are attained by combining iterative methods, such as Lanczos method and randomized algorithms, with fast matrix-vector products that exploit the structure of Hadamard products. Algorithms are implemented in programming language Julia and a new Julia library for tensors in Tucker format is presented.
Abstract (croatian)
Posljednjih godina tenzorske dekompozicije malog ranga postaju bitan alat u znanstvenom računanju kod rješavanja problema velikih dimenzija linearne i multilinearne algebre, koje ne možemo riješiti klasičnim tehnikama. S obzirom na to da tenzori mogu biti zadani kao rješenja neke algebarske jednadžbe, izuzetno je važno razviti algoritme koji rade direktno s komprimiranim tenzorskim formatima. U ovoj radnji fokusiramo se na Tuckerov format, jednu od najčešćee korištenih reprezentacija malog ranga, i Hadamardov produkt, koji ima veliku ulogu u tenzorskim algoritmima za znanstveno računanje i obradu podataka. Brze algoritme dobili smo kombinirajući iterativne metode, poput Lanczosove metode i randomiziranih algoritama, s brzim matrično-vektorskim množenjem koje se temelji na posebnoj strukturi Hadamardovog produkta. Algoritmi su implementirani u novu Julia biblioteku.
Keywords
Keywords (croatian)
Languageenglish
URN:NBNurn:nbn:hr:217:508763
Study programmeTitle: Mathematics
Study programme type: university
Study level: postgraduate
Academic / professional title: doktor/doktorica znanosti, područje prirodnih znanosti, polje matematika (doktor/doktorica znanosti, područje prirodnih znanosti, polje matematika)
Type of resourceText
Extentvi, 111 str.
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2019-03-21 10:02:06