Κατεύθυνση Εφαρμοσμένα Μαθηματικά
Library of the School of Science

2014-02-26

2014

Ρούπα Παρασκευή

Μαριλένα Μητρούλη Αναπλ. Καθηγήτρια ΕΚΠΑ

Αριθμητικές μέθοδοι εκτίμησης διγραμμικών μορφών και εφαρμογές στην ανάλυση δικτύων

Greek

Numerical Methods for estimating bilinear forms with applications in network analysis

This master is estimating and finding bounds for the bilinear form uTf (A)w,
where A a given matrix, u, w given vectors, f given function, and applications
of these estimates to the networks. Initially, we will mention the mathematical
tools that will be needed in the course of this master. We refer to properties
of symmetric, positive definite and semidefinite matrices and various forms of
factorization matrices. Also, we mention the rules of Gaussian quadrature and
Krylov, Arnoldi and Lanczos methods that are projection methods. Then we will
present how to estimate and calculate the bilinear form uTf (A) w. Initially,
we mention how to compute bounds using a Gaussian quadrature rule.
Additionally, we will calculate bounds using partial spectral factorization of
matrix A. Also, we will use the Kantorovich inequality to estimate the diagonal
elements of the inverse of a matrix A and we introduce a family of estimates
for elements of inverse of a matrix A using the method of extrapolation.
Finally, we present some basic definitions for networks and the definition of
the most "important node" and will see how we can find the "most important"
nodes in a network.

Bilinear form, Gaussian quadrature, Kantorovich inequalities, Extrapolation, Networks

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https://pergamos.lib.uoa.gr/uoa/dl/object/1316400