Abstract
Taking the weighted geometric mean (11) on the cone of positive definite ma- trix, we propose an iterative mean algorithm involving weighted arithmetic and geometric means of n positive definite matrices which is a weighted version of Carlson mean pre- sented 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 multidi- mensional versions of all properties like permutation symmetry, concavity, monotonicity, homogeneity, congruence invariancy, duality, mean inequalities.
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