The present article studies the problemof computing empiricalmeans on pseudo-orthogonal groups. To design numerical algorithms to compute empirical means, the pseudo-orthogonal group is endowed with a pseudo-Riemannian metric that affords the computation of the exponential map in closed forms. The distance between two pseudo-orthogonal matrices, which is an essential ingredient, is computed by both the Frobenius norm and the geodesic distance. The empirical-mean computation problem is solved via a pseudo-Riemannian-gradient-stepping algorithm. Several numerical tests are conducted to illustrate the numerical behavior of the devised algorithm.

Empirical means on pseudo-orthogonal groups / Wang, J.; Sun, H.; Fiori, S.. - In: MATHEMATICS. - ISSN 2227-7390. - ELETTRONICO. - 7:10(2019), p. 940. [10.3390/math7100940]

Empirical means on pseudo-orthogonal groups

Fiori S.
2019-01-01

Abstract

The present article studies the problemof computing empiricalmeans on pseudo-orthogonal groups. To design numerical algorithms to compute empirical means, the pseudo-orthogonal group is endowed with a pseudo-Riemannian metric that affords the computation of the exponential map in closed forms. The distance between two pseudo-orthogonal matrices, which is an essential ingredient, is computed by both the Frobenius norm and the geodesic distance. The empirical-mean computation problem is solved via a pseudo-Riemannian-gradient-stepping algorithm. Several numerical tests are conducted to illustrate the numerical behavior of the devised algorithm.
2019
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11566/274509
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