Unit:
Τομέας Άλγεβρας ΓεωμετρίαςLibrary of the School of Science
Supervisors info:
Αναπλ. Καθηγήτρια Μαριλένα Μητρούλη (επιβλέπουσα), Καθηγητής Βασίλειος Δούγαλης, Αναπλ. Καθηγητής Σωτήριος Νοτάρης
Original Title:
Αριθμητικός υπολογισμός του ίχνους αντιστρόφου πίνακα και σχετικές ανισότητες
Translated title:
Numerical computation of the trace of inverse matrix and related inequalities
Summary:
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.
Keywords:
Trace, Extrapolation, Matrix moments, Matrix inverse
File:
File access is restricted only to the intranet of UoA.
document.pdf
581 KB
File access is restricted only to the intranet of UoA.