Original scientific paper
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
Abstract
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.
Keywords
Convex function; Bregman-divergence; Burbea-Rao divergence; exponential convexity; Cauchy means
Hrčak ID:
104401
URI
Publication date:
27.6.2013.
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