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http://dx.doi.org/10.14317/jami.2015.379

A NEW PROOF TO CONSTRUCT MULTIVARIABLE GEOMETRIC MEANS BY SYMMETRIZATION†  

KIM, SEJONG (Department of Mathematics, Chungbuk National University)
PETZ, DENES (Department of Mathematics, Chungbuk National University)
Publication Information
Journal of applied mathematics & informatics / v.33, no.3_4, 2015 , pp. 379-386 More about this Journal
Abstract
The original geometric mean of two positive definite operators A and B is given by A#B = A1/2(A-1/2BA-1/2)1/2A1/2. In this article we provide a new proof to construct from the two-variable geometric mean to the multivariable mean via symmetrization introduced by Lawson and Lim [5]. Finally we provide an algorithm to find three-variable geometric mean via symmetrization, which plays an important role to construct higher-order geometric means.
Keywords
positive definite operator; operator mean;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
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