Weighted Carlson Mean of Positive Definite Matrices

• Journal title : Kyungpook mathematical journal
• Volume 53, Issue 3,  2013, pp.479-495
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2013.53.3.479
Title & Authors
Weighted Carlson Mean of Positive Definite Matrices
Lee, Hosoo;

Abstract
Taking the weighted geometric mean [11] on the cone of positive definite matrix, we propose an iterative mean algorithm involving weighted arithmetic and geometric means of $\small{n}$-positive definite matrices which is a weighted version of Carlson mean presented by Lee and Lim [13]. We show that each sequence of the weigthed Carlson iterative mean algorithm has a common limit and the common limit of satisfies weighted multidimensional versions of all properties like permutation symmetry, concavity, monotonicity, homogeneity, congruence invariancy, duality, mean inequalities.
Keywords
Positive definite matrix;matrix geometric mean;iterative mean algorithm;weighted symmetrization procedure;
Language
English
Cited by
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