Continued fraction representations of the generalized operator entropy

TL;DR

This paper introduces a practical method for calculating the generalized operator entropy using matrix continued fractions, overcoming previous computational difficulties, and also derives a continued fraction expansion for Bregman operator divergence.

Contribution

It presents a novel approach to compute generalized operator entropy via matrix continued fractions and extends this to Bregman operator divergence.

Findings

Efficient calculation method for generalized operator entropy.

Continued fraction expansion of Bregman operator divergence.

Numerical examples demonstrating the method's effectiveness.

Abstract

The direct calculation of the Generalized operator entropy proves difficult by 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 paper, we deduce a continued fraction expansion of the Bregman operator divergence. Some numerical examples illutrating the theoretical result are discussed.