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master's thesis
Konvergencija cikličke Jacobijeve metode za hermitsku matricu reda 4
Zagreb: University of Zagreb, Faculty of Science, 2016. urn:nbn:hr:217:523430
Valentić, Grgur
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

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Valentić, G. (2016). Konvergencija cikličke Jacobijeve metode za hermitsku matricu reda 4 (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:523430

Valentić, Grgur. "Konvergencija cikličke Jacobijeve metode za hermitsku matricu reda 4." Master's thesis, University of Zagreb, Faculty of Science, 2016. https://urn.nsk.hr/urn:nbn:hr:217:523430

Valentić, Grgur. "Konvergencija cikličke Jacobijeve metode za hermitsku matricu reda 4." Master's thesis, University of Zagreb, Faculty of Science, 2016. https://urn.nsk.hr/urn:nbn:hr:217:523430

Valentić, G. (2016). 'Konvergencija cikličke Jacobijeve metode za hermitsku matricu reda 4', Master's thesis, University of Zagreb, Faculty of Science, accessed 02 October 2024, https://urn.nsk.hr/urn:nbn:hr:217:523430

Valentić G. Konvergencija cikličke Jacobijeve metode za hermitsku matricu reda 4 [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2016 [cited 2024 October 02] Available at: https://urn.nsk.hr/urn:nbn:hr:217:523430

G. Valentić, "Konvergencija cikličke Jacobijeve metode za hermitsku matricu reda 4", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2016. Available at: https://urn.nsk.hr/urn:nbn:hr:217:523430

Metadata
TitleKonvergencija cikličke Jacobijeve metode za hermitsku matricu reda 4
AuthorGrgur Valentić
MentorVjeran Hari (mentor)
Committee memberVjeran Hari (predsjednik povjerenstva)
Committee memberLuka Grubišić (član povjerenstva)
Committee memberVjekoslav Kovač (član povjerenstva)
Committee memberMladen Vuković (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2016-09-27, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom radu prikazali smo Jacobijevu metodu za hermitske matrice reda 4 definiranu općom cikličkom pivotnom strategijom. Uveli smo relacije ekvivalencije \(\sim, \underaccent{\tilde}{s}, \underaccent{\tilde}{w}, \underaccent{\tilde}{p}\) na skupu svih cikličkih strategija te pokazali da konvergenost metode pod nekom strategijom povlači konvergentnost metode pod njoj ekvivalentnom strategijom. Zatim smo pokazali globalnu konvergenciju metode pod strategijama iz specijalne familije \(C_1\) te pod jednom paralelnom strategijom. Pomoću računalnog programa podijelili smo 720 cikličkih strategija u 5 klasa ekvivalencije, te u svakoj klasi pronašli strategiju za koju smo pokazali globalnu konvergenciju. To je bilo dovoljno da se pokaže globalna konvergencija metode pod svih 720 cikličkih strategija.
Abstract (english)
In this work we have presented the Jacobi method for Hermitian matrices of order 4 defined by a general cyclic pivot strategy. We have introduced equivalence relations \(\sim, \underaccent{\tilde}{s}, \underaccent{\tilde}{w}, \underaccent{\tilde}{p}\) on the set of cyclic strategies and shown that convergence of the method under some strategy implies convergence of the method under an equivalent strategy. Then we have shown the global convergence of the method under the strategies from the special family \(C_1\) and under one parallel strategy. Using a computer program, we have partitioned the set of 720 cyclic strategies in 5 equivalence classes. For each class we have found a strategy for which the method is convergent. That is enough to show the global convergence of the method under all 720 cyclic strategies.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:523430
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 on2019-02-18 13:04:13