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master's thesis
Numeričko rješavanje linearnih sustava
Zagreb: University of Zagreb, Faculty of Science, 2018. urn:nbn:hr:217:967905
Mikec, Karla
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Mikec, K. (2018). Numeričko rješavanje linearnih sustava (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:967905

Mikec, Karla. "Numeričko rješavanje linearnih sustava." Master's thesis, University of Zagreb, Faculty of Science, 2018. https://urn.nsk.hr/urn:nbn:hr:217:967905

Mikec, Karla. "Numeričko rješavanje linearnih sustava." Master's thesis, University of Zagreb, Faculty of Science, 2018. https://urn.nsk.hr/urn:nbn:hr:217:967905

Mikec, K. (2018). 'Numeričko rješavanje linearnih sustava', Master's thesis, University of Zagreb, Faculty of Science, accessed 03 November 2024, https://urn.nsk.hr/urn:nbn:hr:217:967905

Mikec K. Numeričko rješavanje linearnih sustava [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2018 [cited 2024 November 03] Available at: https://urn.nsk.hr/urn:nbn:hr:217:967905

K. Mikec, "Numeričko rješavanje linearnih sustava", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2018. Available at: https://urn.nsk.hr/urn:nbn:hr:217:967905

Metadata
TitleNumeričko rješavanje linearnih sustava
AuthorKarla Mikec
MentorMarko Erceg (mentor)
Committee memberMarko Erceg (predsjednik povjerenstva)
Committee memberMarko Vrdoljak (član povjerenstva)
Committee memberMiljenko Huzak (član povjerenstva)
Committee memberNenad Antonić (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2018-09-24, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Za rješavanje linearnih sustava jednadžbi postoji nekoliko metoda. Neke od njih su direktne (Gaussove eliminacije, LR faktorizacija) i daju točno rješenje do na pogrešku u zaokruživanju računala, ali nisu praktične za veće sustave jer imaju kubnu složenost. S druge strane su iterativne metode (Jacobijeva, Gauss-Seidelova) koje su brže i efikasne za veće sustave, ali daju aproksimaciju rješenja i u nekim slučajevima sporo konvergiraju prema egzaktnom rješenju. Odabir bolje metode ovisi o danom problemu. U ovom radu su obrađene neke direktne i iterativne metode, te je prezentirana njihova usporedba na primjeru rješavanja diferencijalne jednadžbe. Svi prezentirani algoritmi zapisani su u programskom jeziku Python 3.6.
Abstract (english)
There are several methods for solving linear systems of equations. Some of them are direct (Gaussian Elimination, LR Decomposition) and provide the exact solution neglecting the roundoff error caused by the computer, but they are not practical for solving large systems because their complexity is cubic. On the other side, there are iterative methods (Jacobi, Gauss-Seidel) which are faster and more efficient to use in large systems, but they give approximate solutions and their convergence to the exact solution can be slow. Choosing a better method depends on a given problem. This thesis deals with some of direct and iterative methods, and shows their comparison on the example of solving differential equations. All presented algorithms are written in a programming language Python 3.6.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:967905
Study programmeTitle: Mathematics Education; specializations in: Mathematics Education
Course: Mathematics Education
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2019-06-07 12:41:24