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Weighted geometric means
-
Jimmie Lawson
,
Hosoo Lee
Published/Copyright:
September 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.
Keywords: Matrix geometric mean; positive
definite matrix; Bini–Meini–Poloni symmetrization procedure; convex
metric; weighted mean
Received: 2010-02-26
Published Online: 2012-09-01
Published in Print: 2012-09-01
© 2012 by Walter de Gruyter Berlin Boston
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- Higher integrability in parabolic obstacle problems
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Keywords for this article
Matrix geometric mean;
positive
definite matrix;
Bini–Meini–Poloni symmetrization procedure;
convex
metric;
weighted mean
Articles in the same Issue
- Masthead
- Conjugacy in normal subgroups of hyperbolic groups
- Surgery obstructions on closed manifolds and the inertia subgroup
- Higher integrability in parabolic obstacle problems
- Fundamental solutions for sum of squares of vector fields operators with C1,α coefficients
- Kuykian fields
- Multivariable manifold calculus of functors
- Weighted geometric means
- Kaplansky classes, finite character and ℵ1-projectivity
