A note on computing matrix geometric means

DOI10.1007/s10444-010-9165-0zbMath1293.65068OpenAlexW2082088153MaRDI QIDQ652564

Dario Andrea Bini, Bruno Iannazzo

Publication date: 14 December 2011

Published in: Advances in Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10444-010-9165-0

zbMATH Keywords

geodesicmatrix functionmatrix geometric meanRiemannian centroid

Mathematics Subject Classification ID

Determinants, permanents, traces, other special matrix functions (15A15) Positive matrices and their generalizations; cones of matrices (15B48)

Related Items

Computing the Karcher mean of symmetric positive definite matrices, Geometric means of quasi-Toeplitz matrices, Computing the Weighted Geometric Mean of Two Large-Scale Matrices and Its Inverse Times a Vector, Factorizations and geometric means of positive definite matrices, An algorithm for computing geometric mean of two Hermitian positive definite matrices via matrix sign, Geometric means of structured matrices, The Derivative of the Matrix Geometric Mean with an Application to the Nonnegative Decomposition of Tensor Grids, A geometric mean for Toeplitz and Toeplitz-block block-Toeplitz matrices, Matrix geometric means based on shuffled inductive sequences, Algorithms for approximating means of semi-infinite quasi-Toeplitz matrices

Uses Software

• Matrix Means Toolbox
• mftoolbox

Cites Work

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• Riemannian geometry and matrix geometric means
• Functional calculus for sesquilinear forms and the purification map
• Geometric means
• On the averaging of symmetric positive-definite tensors
• Constructing matrix geometric means
• An effective matrix geometric mean satisfying the Ando–Li–Mathias properties
• The Geometric Mean, Matrices, Metrics, and More
• A Differential Geometric Approach to the Geometric Mean of Symmetric Positive-Definite Matrices
• Functions of Matrices