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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

Puni tekst: engleski, pdf (335 KB) str. 11-32 preuzimanja: 269* citiraj
APA 6th Edition
Khan, M.A., Niezgoda, M. i Pečarić, J. (2013). Bregman and Burbea-Rao divergence for matrices. Rad Hrvatske akademije znanosti i umjetnosti, (515=17), 11-32. Preuzeto s https://hrcak.srce.hr/104401
MLA 8th Edition
Khan, M. Adil, et al. "Bregman and Burbea-Rao divergence for matrices." Rad Hrvatske akademije znanosti i umjetnosti, vol. , br. 515=17, 2013, str. 11-32. https://hrcak.srce.hr/104401. Citirano 10.08.2020.
Chicago 17th Edition
Khan, M. Adil, M. Niezgoda i Josip Pečarić. "Bregman and Burbea-Rao divergence for matrices." Rad Hrvatske akademije znanosti i umjetnosti , br. 515=17 (2013): 11-32. https://hrcak.srce.hr/104401
Harvard
Khan, M.A., Niezgoda, M., i Pečarić, J. (2013). 'Bregman and Burbea-Rao divergence for matrices', Rad Hrvatske akademije znanosti i umjetnosti, (515=17), str. 11-32. Preuzeto s: https://hrcak.srce.hr/104401 (Datum pristupa: 10.08.2020.)
Vancouver
Khan MA, Niezgoda M, Pečarić J. Bregman and Burbea-Rao divergence for matrices. Rad Hrvatske akademije znanosti i umjetnosti [Internet]. 2013 [pristupljeno 10.08.2020.];(515=17):11-32. Dostupno na: https://hrcak.srce.hr/104401
IEEE
M.A. Khan, M. Niezgoda i J. Pečarić, "Bregman and Burbea-Rao divergence for matrices", Rad Hrvatske akademije znanosti i umjetnosti, vol., br. 515=17, str. 11-32, 2013. [Online]. Dostupno na: https://hrcak.srce.hr/104401. [Citirano: 10.08.2020.]

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

Projekti
MZOS / ZP / 117-1170889-0888 - Generalne nejednakosti i primjene

Hrčak ID: 104401

URI
https://hrcak.srce.hr/104401

Posjeta: 380 *