Carlson's iterative mean algorithm of positive definite matrices

DOI10.1016/j.laa.2013.04.005zbMath1305.65132OpenAlexW1968468079MaRDI QIDQ389582

Yongdo Lim, Ho Soo Lee

Publication date: 21 January 2014

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

Full work available at URL: https://doi.org/10.1016/j.laa.2013.04.005

zbMATH Keywords

positive definite matrixKarcher meanmatrix geometric meanALM and BMP symmetrization procedureiterative mean algorithm

Mathematics Subject Classification ID

Positive matrices and their generalizations; cones of matrices (15B48) Subgroups of symmetric groups (20B35) Operator means involving linear operators, shorted linear operators, etc. (47A64)

Cites Work

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• Monotonic properties of the least squares mean
• Riemannian geometry and matrix geometric means
• Means of positive linear operators
• Convexity of the geodesic distance on spaces of positive operators
• On the exponential metric increasing property.
• Invariant means
• Geometric means
• Karcher means and Karcher equations of positive definite operators
• An effective matrix geometric mean satisfying the Ando–Li–Mathias properties
• Matrix Analysis
• [https://portal.mardi4nfdi.de/wiki/Publication:3829784 On the Mean Iteration (a, b) ← � � a+3b 4 , √ab+b 2 � �]
• Self-Scaled Barriers and Interior-Point Methods for Convex Programming
• The Geometric Mean, Matrices, Metrics, and More
• A Cubic Counterpart of Jacobi's Identity and the AGM
• A Differential Geometric Approach to the Geometric Mean of Symmetric Positive-Definite Matrices
• Invariant metrics, contractions and nonlinear matrix equations
• Means of Positive Numbers and Matrices
• On Certain Contraction Mappings in a Partially Ordered Vector Space
• Hidden Symmetries of Special Functions
• Algorithms Involving Arithmetic and Geometric Means