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undergraduate thesis
Geršgorinovi krugovi
Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2020. urn:nbn:hr:126:728012
Mađarić, Lea
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Applied Mathematics
Numerical Mathematics Research Group

Cite this document

Mađarić, L. (2020). Geršgorinovi krugovi (Undergraduate thesis). Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:728012

Mađarić, Lea. "Geršgorinovi krugovi." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2020. https://urn.nsk.hr/urn:nbn:hr:126:728012

Mađarić, Lea. "Geršgorinovi krugovi." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2020. https://urn.nsk.hr/urn:nbn:hr:126:728012

Mađarić, L. (2020). 'Geršgorinovi krugovi', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 23 March 2023, https://urn.nsk.hr/urn:nbn:hr:126:728012

Mađarić L. Geršgorinovi krugovi [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2020 [cited 2023 March 23] Available at: https://urn.nsk.hr/urn:nbn:hr:126:728012

L. Mađarić, "Geršgorinovi krugovi", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2020. Available at: https://urn.nsk.hr/urn:nbn:hr:126:728012

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Metadata
TitleGeršgorinovi krugovi
Title (english)Gershgorin's Discs
AuthorLea Mađarić
MentorIvana Kuzmanović Ivičić (mentor)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
(Chair of Applied Mathematics)
(Numerical Mathematics Research Group)
Osijek
Defense date and country2020-09-30, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Algebra
Abstract
U ovom radu razmatramo problem približnog lociranja područja u Gaussovoj ravnini unutar kojeg leži spektar kompleksne kvadratne matrice. Za poznavanje spektra kvadratne matrice potrebno je odrediti njene svojstvene vrijednosti, a sam postupak njihovog određivanja opisan je u prvom poglavlju. Za matrice većeg reda računanje svojstvenih vrijednosti može biti vrlo zahtjevno. U nekim primjenama dovoljno je spektar samo približno locirati. Geršgorinov poznati teorem govori o tome kako sve svojstvene vrijednosti kvadratne matrice leže u krugovima, zvanim Geršgorinovi krugovi, oko dijagonalnih elemenata. Za neke specijalne slučajeve, moguće je iskoristiti danu strukturu i odrediti još i manje krugove koji sadrže svojstvene vrijednosti od onih iz općenitog Gešgorinovog rezultata. Tvrdnje su potkrijepljene primjerima koji vjerno prikazuju sadžaj Gešgorinovih teorema.
Abstract (english)
In this paper, we consider the problem of determining a subset of the complex plane which contains all eigenvalues of the given complex matrix.To know the spectrum of a square matrix, it is necessary to determine its eigenvalues, and the procedure for their determination is described in the first chapter. For higher order matrices, the calculation of eigenvalues can be very demanding. In some applications, it is sufficient to locate the spectrum only approximately. Gershgorin’s well-known theorem states that all eigenvalues of a square matrix lie in disks, called Gershgorin disks, around the diagonal elements. For some special cases, it is possible to use a given structure and determine even smaller circles that contain eigenvalues than those from the general Gershgorin result. The claims are supported by examples that faithfully illustrate the content of Gershgorin’s theorems.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:728012
Study programmeTitle: University undergraduate study programme in mathematics
Study programme type: university
Study level: undergraduate
Academic / professional title: sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike (sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
RepositoryRepository of Department of Mathematics Osijek
Created on2020-11-13 09:50:36