Weighted geometric means

DOI10.1515/form.2011.096zbMath1275.47040OpenAlexW2334854526MaRDI QIDQ3165877

Yongdo Lim, Jimmie D. Lawson, Ho Soo Lee

Publication date: 19 October 2012

Published in: Forum Mathematicum (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/form.2011.096

zbMATH Keywords

positive definite matrixweighted meanmatrix geometric meanconvex metricBini-Meini-Poloni symmetrization procedure

Mathematics Subject Classification ID

Metric spaces, metrizability (54E35) Metric geometry (51F99) Positive matrices and their generalizations; cones of matrices (15B48) Operator means involving linear operators, shorted linear operators, etc. (47A64)

Related Items (15)

An order inequality characterizing invariant barycenters on symmetric cones ⋮ Loewner's theorem in several variables ⋮ An elementary proof of arithmetic-geometric mean inequality of the weighted Riemannian mean of positive definite matrices ⋮ Geometric means of quasi-Toeplitz matrices ⋮ Multi-variable weighted geometric means of positive definite matrices ⋮ Monotonic properties of the least squares mean ⋮ Factorizations and geometric means of positive definite matrices ⋮ Convex geometric means ⋮ Ordered probability spaces ⋮ A fixed point mean approximation to the Cartan barycenter of positive definite matrices ⋮ Convergence theorems for barycentric maps ⋮ Moving averages on convex metric spaces ⋮ Weighted multivariable operator means of positive definite operators ⋮ Geometries on the cone of positive-definite matrices derived from the power potential and their relation to the power means ⋮ Weighted inductive means

Cites Work

• Riemannian geometry and matrix geometric means
• Invariant means
• Geometric means
• An effective matrix geometric mean satisfying the Ando–Li–Mathias properties
• Symmetric spaces with convex metrics

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