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Continued Fraction Expansion of the Heinz Operator Mean
American Journal of Applied Mathematics
Volume 8, Issue 6, December 2020, Pages: 311-318
Received: Jul. 17, 2020; Accepted: Sep. 9, 2020; Published: Dec. 6, 2020
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Kacem Belhroukia, Department of Mathematics, Science Faculty, Ibn Toufail University, Kenitra, Morocco
Salah Salhi, Department of Mathematics, Regional Center for Education and Training Professions, Errachidia, Morocco
Ali Kacha, Department of Mathematics, Science Faculty, Ibn Toufail University, Kenitra, Morocco
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We recall that means arise in various contexts and contribute to solving many scientific problems. The aim of the present paper is to give a continued fraction expansion of the Heinz operator mean for two positive definite matrices. We note that the direct calculation of the Heinz operator mean 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. We use the matrix continued fraction algorithm. At the end of our paper, we deduce a continued fraction representation of the symmetric operator entropy.
Continued Fraction, Positive Definite Matrix, Heinz Operator Mean
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Kacem Belhroukia, Salah Salhi, Ali Kacha, Continued Fraction Expansion of the Heinz Operator Mean, American Journal of Applied Mathematics. Vol. 8, No. 6, 2020, pp. 311-318. doi: 10.11648/j.ajam.20200806.13
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This article is an open access article distributed under the Creative Commons Attribution License ( which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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