Continued Fraction Representation of the Generalized Operator Entropy

EasyChair Preprint 7881

Abstract

Recently, the extension of continued fractions theory from real numbers to the matrix case has seen several development and interesting applications [1,2,3,4]. Since calculations involving matrix valued functions with matrix arguments are feasible with large computers, it will be an interesting attempt to develop such matrix theory. The real case is relatively well studied in the literature [7,8]. However, in contrast to the theoretical importance, one can find in mathematical literature only a few results on the continued fractions with matrix argument [5,6]. 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 [10,11].

Keyphrases: Entropy, Generalized, operator

@booklet{EasyChair:7881,
  author    = {Ali Kacha and Sarra Ahallal and Said Mennou},
  title     = {Continued Fraction Representation of the Generalized Operator Entropy},
  howpublished = {EasyChair Preprint 7881},
  year      = {EasyChair, 2022}}