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master's thesis
Numeričko rješavanje linearnih matričnih jednadžbi
Zagreb: University of Zagreb, Faculty of Science, 2016. urn:nbn:hr:217:559029
Šestan, Jasmina
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Šestan, J. (2016). Numeričko rješavanje linearnih matričnih jednadžbi (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:559029

Šestan, Jasmina. "Numeričko rješavanje linearnih matričnih jednadžbi." Master's thesis, University of Zagreb, Faculty of Science, 2016. https://urn.nsk.hr/urn:nbn:hr:217:559029

Šestan, Jasmina. "Numeričko rješavanje linearnih matričnih jednadžbi." Master's thesis, University of Zagreb, Faculty of Science, 2016. https://urn.nsk.hr/urn:nbn:hr:217:559029

Šestan, J. (2016). 'Numeričko rješavanje linearnih matričnih jednadžbi', Master's thesis, University of Zagreb, Faculty of Science, accessed 16 May 2024, https://urn.nsk.hr/urn:nbn:hr:217:559029

Šestan J. Numeričko rješavanje linearnih matričnih jednadžbi [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2016 [cited 2024 May 16] Available at: https://urn.nsk.hr/urn:nbn:hr:217:559029

J. Šestan, "Numeričko rješavanje linearnih matričnih jednadžbi", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2016. Available at: https://urn.nsk.hr/urn:nbn:hr:217:559029

Metadata
TitleNumeričko rješavanje linearnih matričnih jednadžbi
AuthorJasmina Šestan
MentorZvonimir Bujanović (mentor)
Committee memberZvonimir Bujanović (predsjednik povjerenstva)
Committee memberBoris Muha (član povjerenstva)
Committee memberJosip Tambača (član povjerenstva)
Committee memberNenad Antonić (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2016-04-27, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom smo radu dali pregled postojećih rezultata u području numeričkog rješavanja linearnih matričnih jednadžbi na primjeru Sylvesterove i Lyapunovljeve jednadžbe. Naveli smo zašto su od interesa u primijenjenoj matematici, posebno u analizi stabilnosti dinamičkih sustava. Razmotrili smo cesto korišten Bartels–Stewartov algoritam koji je pogodan za rješavanje jednadžbi malih dimenzija. Za matrične jednadžbe velikih dimenzija razmotrili smo iterativne načine rješavanja: metodu ADI iteracija i projekcijsku Krylovljevu metodu. Pritom smo uzeli u obzir strukture matrica koje se često pojavljuju u primjenama. Implementaciju ovih algoritama smo napravili u Pythonu.
Abstract (english)
In this work we reviewed main computational methods for solving linear matrix equations, particularly Sylvester and Lyapunov equations. We explained their role in applied mathematics, especially in stability analysis of linear dynamic systems. We described Bartels–Stewart algorithm which is frequently used for solving matrix equations of small dimensions. For large-scale matrix equations, we considered special structure of matrices which are often encountered in applications and we described iterative methods for finding solution: ADI method and projection (Krylov) method. We implemented listed algorithms using Python.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:559029
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
Created on2019-02-13 11:14:27