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master's thesis
Redukcija modela vođena podacima
Zagreb: University of Zagreb, Faculty of Science, 2021. urn:nbn:hr:217:674545
Kroflin, Matej
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Kroflin, M. (2021). Redukcija modela vođena podacima (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:674545

Kroflin, Matej. "Redukcija modela vođena podacima." Master's thesis, University of Zagreb, Faculty of Science, 2021. https://urn.nsk.hr/urn:nbn:hr:217:674545

Kroflin, Matej. "Redukcija modela vođena podacima." Master's thesis, University of Zagreb, Faculty of Science, 2021. https://urn.nsk.hr/urn:nbn:hr:217:674545

Kroflin, M. (2021). 'Redukcija modela vođena podacima', Master's thesis, University of Zagreb, Faculty of Science, accessed 03 November 2024, https://urn.nsk.hr/urn:nbn:hr:217:674545

Kroflin M. Redukcija modela vođena podacima [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2021 [cited 2024 November 03] Available at: https://urn.nsk.hr/urn:nbn:hr:217:674545

M. Kroflin, "Redukcija modela vođena podacima", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2021. Available at: https://urn.nsk.hr/urn:nbn:hr:217:674545

Metadata
TitleRedukcija modela vođena podacima
Title (english)Data-driven model reduction
AuthorMatej Kroflin
MentorZvonimir Bujanović (mentor)
Committee memberZvonimir Bujanović (predsjednik povjerenstva)
Committee memberDražen Adamović (član povjerenstva)
Committee memberMiljenko Marušić (član povjerenstva)
Committee memberAna Prlić (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2021-04-30, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Ovaj rad se bavi redukcijom modela vođenom podacima koja koristi Loewnerovu matricu i njena svojstva. U prvom poglavlju su definirani osnovni pojmovi vezani uz teoriju sustava te su navedeni neki glavni rezultati te teorije. U drugom poglavlju definira se problem racionalne interpolacije. U nastavku su opisana glavna svojstva i rezultati vezani za Loewnerovu matricu . Na kraju poglavlja proučena je veza Loewnerove matrice i iz nje izvedene racionalne funkcije te je izvedena greška aproksimacije interpolacijske funkcije. U posljednjem poglavlju je obrađen općenitiji slučaj tangencijalne interpolacije i defiran je pojam Loewnerov par. Naveden je općeniti algoritam za redukciju modela pomoću Loewnerovog para. Također su pokazani rezultati primjene algoritma na sustave većih dimenzija čiji su podaci javno dostupni u [8].
Abstract (english)
This thesis deals with the processing of model reduction using the Loewner matrix and its properties. The first chapter defines the basic concepts related to system theory and presents some main results of that theory. The second chapter defines the problem of rational interpolation. The main properties and results related to the Loewner matrix are described. At the end of the chapter, the connection between the Loewner matrix and the rational function is studied, and the error of approximation of the interpolation function is derived. In the last chapter, a more general case of tangential interpolation is treated and the Loewner pair is defined.A generalized algorithm for model reduction using the Loewner pair is presented. Finally, numerical results demonstrate the effectiveness of the algorithm by applying it to publicaly available [8] systems of larger dimension.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:674545
Study programmeTitle: Applied Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2021-05-19 11:43:23