Continued Fraction Representations of the Generalized Operator Entropy

Sarra Ahallal; Ali Kacha; Said Mennou

doi:10.2478/tmmp-2023-0024

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Continued Fraction Representations of the Generalized Operator Entropy

Tatra Mountains Mathematical Publications

Volume 85 (2023): Issue 3 (November 2023)

By: Sarra Ahallal, Ali Kacha and Said Mennou

Open Access

|Nov 2023

Abstract

The direct calculation of the generalized operator entropy proves to be difficult due to the appearance of rational exponents of matrices. The main motivation of this work is to overcome these difficulties and to present a practical and efficient method for this calculation using its representation by the matrix continued fraction. At the end of our work, we deduce a continued fraction expansion of the Bregman operator divergence. Some numerical examples illustrating the theoretical result are discussed.

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Articles in this issue

DOI: https://doi.org/10.2478/tmmp-2023-0024 | Journal eISSN: 1338-9750 | Journal ISSN: 1210-3195

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Language: English

Page range: 57 - 72

Submitted on: Oct 19, 2022

Published on: Nov 16, 2023

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

continued fractions,

representation,

generalized operator entropy

Related subjects:

Mathematics,

General mathematics

© 2023 Sarra Ahallal, Ali Kacha, Said Mennou, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 85 (2023): Issue 3 (November 2023)