Weighted geometric means

Document Type

Article

Publication Date

9-1-2012

Abstract

Taking a weighted version of Bini-Meini-Poloni symmetrization procedure for a multivariable geometric mean, we propose a definition for a weighted geometric mean of n positive definite matrices, where the weights vary over all n-dimensional positive probability vectors. We show that the weighted mean satisfies multidimensional versions of all properties that one would expect for a two-variable weighted geometric mean. Significant portions of the derivation can be and are carried out in general convex metric spaces, which means that the results have broader application than the setting of positive definite matrices. © de Gruyter 2012.

Publication Source (Journal or Book title)

Forum Mathematicum

First Page

1067

Last Page

1090

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