Izvorni znanstveni članak

Bregman and Burbea-Rao divergence for matrices

M. Adil Khan ; Abdus Salam School of Mathematical Sciences, GC University, Lahore, Pakistan
M. Niezgoda ; Department of Applied Mathematics and Computer Science, University of Life Sciences in Lublin, Poland
Josip Pečarić ; University of Zagreb, Faculty of Textile Technology Zagreb, Croatia

Sažetak

In this paper, the Bregman and Burbea-Rao divergences
for matrices are investigated. Two mean-value theorems
for the divergences induced by C^2-functions are derived. As application,
certain Cauchy type means of the entries of the matrices
are constructed. By utilizing three classes of parametrized convex
functions, the exponential convexity of the divergences, thought as
a function of the parameter, is proved. The monotonicity of the
corresponding means of Cauchy type is shown. Power means are
also considered.

Ključne riječi

Convex function; Bregman-divergence; Burbea-Rao divergence; exponential convexity; Cauchy means

Hrčak ID:

104401

URI

https://hrcak.srce.hr/104401

Datum izdavanja:

27.6.2013.

Posjeta: 859 *