Στοχαστικοί εκτιμητές του ίχνους συναρτήσεων πινάκων

Φίκα, Παρασκευή; Fika, Paraskevi

dc.contributor.author	Φίκα, Παρασκευή	el
dc.contributor.author	Fika, Paraskevi	en
dc.date.accessioned	2017-01-13T09:10:37Z
dc.date.available	2017-01-13T09:10:37Z
dc.date.issued	2017-01-13
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/44200
dc.identifier.uri	http://dx.doi.org/10.26240/heal.ntua.6318
dc.rights	Default License
dc.subject	Στοχαστικός εκτιμητής	el
dc.subject	Ίχνος	el
dc.subject	Συνάρτηση πίνακα	el
dc.title	Στοχαστικοί εκτιμητές του ίχνους συναρτήσεων πινάκων	el
heal.type	masterThesis
heal.classification	ΜΑΘΗΜΑΤΙΚΑ	el
heal.classificationURI	http://data.seab.gr/concepts/da4b9237bacccdf19c0760cab7aec4a8359010b0
heal.language	el
heal.access	free
heal.recordProvider	ntua	el
heal.publicationDate	2016-03-02
heal.abstract	In this postgraduate work, stochastic estimates for the trace of functions of matrices, denoted as Tr(f(A)), are developed, where f is a suitable function and A is a symmetric matrix. This aims to the avoidance of the explicit computation of the matrix f(A). The trace of a matrix function arises in many disciplines such as in physics, in statistics, in network analysis, etc. The computation of a function of a matrix A can have a high computational cost, especially for large matrices that are required in applications. Therefore, it is necessary to estimate the trace of f(A). Stochastic estimates have been proposed, which are based on the computation of the quantity \sum_1^N x_i^T f(A)x_i /N for different sample vectors x_i, where N is the sample size (the number of the sample vectors). It can be proved that the expected value of the quantity x^T f(A)x, for suitable vector x and symmetric matrix A, equals to the Tr(f(A)). Moreover, since the proposed estimates are of a statistical nature, it is natural to expect that the application of some statistical designs may improve their quality and their effectiveness in estimating the trace Tr(f(A)). Various statistical designs will be compared and numerical examples stemming from real applications will be discussed.	en
heal.advisorName	Κουκουβίνος, Χρήστος	el
heal.committeeMemberName	Βόντα, Φιλία	el
heal.committeeMemberName	Σπηλιώτης, Ιωάννης	el
heal.committeeMemberName	Κουκουβίνος, Χρήστος	el
heal.academicPublisher	Εθνικό Με5τσόβιο Πολυτεχνείο. Σχολή Εφαρμοσμένων Μαθηματικών και Φυσικών Επιστημών	el
heal.academicPublisherID	ntua
heal.numberOfPages	78 σ.	el
heal.fullTextAvailability	true