Τομέας Άλγεβρας Γεωμετρίας
Library of the School of Science

2014-03-12

2014

Φίκα Παρασκευή

Αναπλ. Καθηγήτρια Μαριλένα Μητρούλη (επιβλέπουσα), Καθηγητής Βασίλειος Δούγαλης, Αναπλ. Καθηγητής Σωτήριος Νοτάρης

Αριθμητικός υπολογισμός του ίχνους αντιστρόφου πίνακα και σχετικές ανισότητες

Greek

Numerical computation of the trace of inverse matrix and related inequalities

In this work, an extrapolation method estimating the quadratic form x^t Α^(-
1) x is developed, using as mathematical tools the spectral decomposition of
matrix A and its moments. In the sequel, estimates for the trace of the inverse
of matrix A, Tr(Α^(-1) ), are risen, since it holds that the expected value of
the quantity x^t Α^(-1) x equals the trace of the matrixΑ^(-1), for suitably
chosen vector x. Estimates for Tr(Α^(-1) ), for symmetric and non symmetric
matrices, as well as upper an lower bounds for the quantitiesx^t Α^(-1) xand
Tr(Α^(-1)) are presented. Moreover the computational complexity of the
estimates is discussed and statistical techniques are proposed in order to
improve the quality of the estimates.

Trace, Extrapolation, Matrix moments, Matrix inverse

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https://pergamos.lib.uoa.gr/uoa/dl/object/1316406