The Derivative of the Matrix Geometric Mean with an Application to the Nonnegative Decomposition of Tensor Grids

DOI10.1007/978-3-030-04088-8_6zbMath1445.15017OpenAlexW2938239180MaRDI QIDQ3294687

Ben Jeuris, Filippo Pompili, Bruno Iannazzo

Publication date: 29 June 2020

Published in: Structured Matrices in Numerical Linear Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-030-04088-8_6

zbMATH Keywords

positive definite matrixKarcher meanmatrix geometric meannonnegative factorizationtensor grid

Mathematics Subject Classification ID

Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Means (26E60) Operator means involving linear operators, shorted linear operators, etc. (47A64)

Related Items (3)

On Multiscale Quasi-Interpolation of Scattered Scalar- and Manifold-Valued Functions ⋮ Geometric means of quasi-Toeplitz matrices ⋮ Geometries on the cone of positive-definite matrices derived from the power potential and their relation to the power means

Uses Software

• Matrix Means Toolbox
• mftoolbox

Cites Work

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• Computing the Karcher mean of symmetric positive definite matrices
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• On the averaging of symmetric positive-definite tensors
• A Novel Dynamic System in the Space of SPD Matrices with Applications to Appearance Tracking
• The Riemannian Barzilai–Borwein method with nonmonotone line search and the matrix geometric mean computation
• Weighted means and Karcher equations of positive operators
• Functions of Matrices
• The geometric mean of two matrices from a computational viewpoint

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