Continued fraction representations of the generalized operator entropy

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.