<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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.</p>
</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.

Continued Fraction Representations of the Generalized Operator Entropy

University of Ibn Tofail Laboratory EDPAGS

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"Continued Fraction Representations of the Generalized Operator Entropy"}

The direct calculation of the generalized operator entropy proves to be difficult due to the appearance of rational exponents of matrices. The main motivation...

Continued Fraction Representations of the Generalized Operator Entropy

Published Online: Nov 16, 2023

Page range: 57 - 72

Received: Oct 19, 2022

DOI: https://doi.org/10.2478/tmmp-2023-0024

Keywords
continued fractions, representation, generalized operator entropy

© 2023 Sarra Ahallal et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Continued Fraction Representations of the Generalized Operator Entropy

Published Online: Nov 16, 2023

Page range: 57 - 72

Received: Oct 19, 2022

DOI: https://doi.org/10.2478/tmmp-2023-0024

Keywordscontinued fractions, representation, generalized operator entropy

© 2023 Sarra Ahallal et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
continued fractions, representation, generalized operator entropy