The geometric mean of two matrices from a computational viewpoint
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Publication:5739758
DOI10.1002/nla.2022zbMath1374.65083arXiv1201.0101OpenAlexW1845326303MaRDI QIDQ5739758
Publication date: 19 July 2016
Published in: Numerical Linear Algebra with Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1201.0101
algorithmsPadé approximationGaussian quadraturepolar decompositionmatrix iterationcyclic reductionmatrix functionmatrix geometric meanrational minimax approximation
Positive matrices and their generalizations; cones of matrices (15B48) Means (26E60) Operator means involving linear operators, shorted linear operators, etc. (47A64) Numerical computation of matrix exponential and similar matrix functions (65F60)
Related Items (18)
Further inequalities involving the weighted geometric operator mean and the Heinz operator mean ⋮ Computing Fundamental Matrix Decompositions Accurately via the Matrix Sign Function in Two Iterations: The Power of Zolotarev's Functions ⋮ On the Matrix Square Root via Geometric Optimization ⋮ Structured condition number for a certain class of functions of non-commuting matrices ⋮ Geometric means of quasi-Toeplitz matrices ⋮ A binomial expansion formula for weighted geometric means of unipotent matrices ⋮ Shift-invariant approximations of structured shift-variant blurring matrices ⋮ Computing the Weighted Geometric Mean of Two Large-Scale Matrices and Its Inverse Times a Vector ⋮ 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 ⋮ Geometric Matrix Midranges ⋮ Krylov iterative methods for the geometric mean of two matrices times a vector ⋮ Computing enclosures for the inverse square root and the sign function of a matrix ⋮ The palindromic cyclic reduction and related algorithms ⋮ Verified computation for the geometric mean of two matrices ⋮ Conditioning of the matrix-matrix exponentiation ⋮ A fixed point mean approximation to the Cartan barycenter of positive definite matrices
Uses Software
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