Redukcija modela vođena podacima

master's thesis

• Title (english): Data-driven model reduction
• Author: Matej Kroflin
• Mentor: Zvonimir Bujanović (mentor)
• Committee member: Zvonimir Bujanović (predsjednik povjerenstva)
• Committee member: Dražen Adamović (član povjerenstva)
• Committee member: Miljenko Marušić (član povjerenstva)
• Committee member: Ana Prlić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2021-04-30, 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: Loewnerova matrica; teorija sustava; Loewnerov par
• Keywords (english): Loewner matrix; system theory; Loewner pair
• Language: croatian
• URN:NBN: urn:nbn:hr:217:674545
• 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: 2021-05-19 11:43:23