The matrix geometric mean of parameterized, weighted arithmetic and harmonic means

DOI10.1016/j.laa.2011.04.010zbMath1222.15036OpenAlexW2031138269MaRDI QIDQ551336

Yongdo Lim, Sejong Kim, Jimmie D. Lawson

Publication date: 15 July 2011

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2011.04.010

zbMATH Keywords

arithmetic meanKullback-Leibler divergencepositive definite matrixweighted meanharmonic meanmatrix meanmatrix geometric meantrace metric

Mathematics Subject Classification ID

Positive matrices and their generalizations; cones of matrices (15B48) Means (26E60) Operator means involving linear operators, shorted linear operators, etc. (47A64)

Related Items (13)

Lie-Trotter means of positive definite operators ⋮ The resolvent average on symmetric cones ⋮ On some inequalities for the matrix power and Karcher means ⋮ Contractive barycentric maps and \(L^{1}\) ergodic theorems on the cone of positive definite matrices ⋮ Mixture and interpolation of the parameterized ordered means ⋮ Logarithmic mean of positive invertible operators ⋮ A geometric mean of parameterized arithmetic and harmonic means of convex functions ⋮ A Proximal Average for Prox-Bounded Functions ⋮ Robust Averaging of Covariances for EEG Recordings Classification in Motor Imagery Brain-Computer Interfaces ⋮ A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means ⋮ Nonexpansiveness of the resolvent average ⋮ The resolvent average on symmetric cones of JB-algebras ⋮ Structure preserving matrix means on the Marcus-Minc stochastic matrices

Cites Work

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• Geometric means
• The resolvent average for positive semidefinite matrices
• On the averaging of symmetric positive-definite tensors
• An effective matrix geometric mean satisfying the Ando–Li–Mathias properties
• The Proximal Average: Basic Theory
• The Geometric Mean, Matrices, Metrics, and More

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