Δίσκοι Geršgorin και Συναφή Χωρία

Μουτζουρέλλης, Ελευθέριος; Moutzourellis, Eleftherios

dc.contributor.author	Μουτζουρέλλης, Ελευθέριος	el
dc.contributor.author	Moutzourellis, Eleftherios	en
dc.date.accessioned	2018-02-15T11:31:43Z
dc.date.available	2018-02-15T11:31:43Z
dc.date.issued	2018-02-15
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/46524
dc.identifier.uri	http://dx.doi.org/10.26240/heal.ntua.14786
dc.rights	Αναφορά Δημιουργού-Μη Εμπορική Χρήση-Όχι Παράγωγα Έργα 3.0 Ελλάδα	*
dc.rights.uri	http://creativecommons.org/licenses/by-nc-nd/3.0/gr/	*
dc.subject	Cassini	en
dc.subject	Geršgorin	en
dc.subject	Brauer	en
dc.subject	Brualdi	en
dc.subject	Ostrowski	en
dc.subject	Ιδιοτιμές	el
dc.subject	Ιδιοδιανύσματα	el
dc.subject	Δίσκοι	el
dc.subject	Οβάλ	el
dc.subject	Λημνίσκοι	el
dc.subject	Ανάλυση πινάκων	el
dc.title	Δίσκοι Geršgorin και Συναφή Χωρία	el
heal.type	bachelorThesis
heal.classification	Μαθηματικά	el
heal.language	el
heal.access	free
heal.recordProvider	ntua	el
heal.publicationDate	2017-10-25
heal.abstract	In this diploma thesis, we will try to approximate the spectrum of complex square matrices by means of some special sets in the field of complex numbers, that are directly dependent on the diagonal elements of the matrix and indirectly from the rest elements. After we first introduce the reader to some basic linear algebra and matrix theory, we will look at the interdependence of the strictly diagonally dominated matrices with these sets. The first theorem that we will present in detail is the Geršgorin theorem. This theorem generates the famous Geršgorin discs, whose union gives the Geršgorin set, an extraordinary, unique and useful set that includes all the eigenvalues of a random complex square table. Then we will quote many extentions of the above theorem via graph theory, borrowing data from the directed graph of matrices. Additionally, we will write about the norm derivation of Geršgorin theorem and examine some of its analytical extensions. Furthermore, we will generalize the eigenvalue inclusion disks to the Cassini ovals and later to some higher order lemniscates. The Brauer set stems from the union of these ovals, while the union of the later, under certain conditions, is defined as the Brualdi set. All sets enclose the spectrum of any matrix, so our penultimate task is to compare them and draw conclusions not only about the area they occupy at the complex field, but also about the computational work that is needed to estimate them. Finally, we will present corollaries and more recent results in an attempt to define the previous sets' sharpness.	en
heal.advisorName	Ψαρράκος, Παναγιώτης	el
heal.committeeMemberName	Αρβανιτάκης, Αλέξανδρος	el
heal.committeeMemberName	Κανελλόπουλος, Βασίλειος	el
heal.academicPublisher	Εθνικό Μετσόβιο Πολυτεχνείο. Σχολή Εφαρμοσμένων Μαθηματικών και Φυσικών Επιστημών. Τομέας Μαθηματικών	el
heal.academicPublisherID	ntua
heal.numberOfPages	74 σ.
heal.fullTextAvailability	true