Diagonality measures of Hermitian positive-definite matrices with application to the approximate joint diagonalization problem
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Publication:1789401
DOI10.1016/j.laa.2016.08.031zbMath1398.15043arXiv1608.06613OpenAlexW2963684104MaRDI QIDQ1789401
Marco Congedo, Khaled Alyani, Maher Moakher
Publication date: 10 October 2018
Published in: Linear Algebra and its Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1608.06613
Kullback-Leibler divergencepositive definite matrixRiemannian distanceapproximate joint diagonalizationdiagonality measure
Positive matrices and their generalizations; cones of matrices (15B48) Hermitian, skew-Hermitian, and related matrices (15B57) Measures of information, entropy (94A17)
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Cites Work
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- Matrix power means and the Karcher mean
- Riemannian geometry and matrix geometric means
- Operator means of probability measures and generalized Karcher equations
- Means of Hermitian positive-definite matrices based on the log-determinant \(\alpha\)-divergence function
- Visualization and processing of tensor fields.
- Joint Approximate Diagonalization of Positive Definite Hermitian Matrices
- Pinching, Trimming, Truncating, and Averaging of Matrices
- Fast Approximate Joint Diagonalization Incorporating Weight Matrices
- A New Algorithm for Complex Non-Orthogonal Joint Diagonalization Based on Shear and Givens Rotations
- An Algorithm for Simultaneous Orthogonal Transformation of Several Positive Definite Symmetric Matrices to Nearly Diagonal Form
- Divergence Function, Duality, and Convex Analysis
- Jacobi Angles for Simultaneous Diagonalization
- Divergence Measures and Means of Symmetric Positive-Definite Matrices
- A Differential Geometric Approach to the Geometric Mean of Symmetric Positive-Definite Matrices
- Newton Method for Joint Approximate Diagonalization of Positive Definite Hermitian Matrices
- Optimization algorithms exploiting unitary constraints
- Non-orthogonal joint diagonalization in the least-squares sense with application in blind source separation
- Geometric Means in a Novel Vector Space Structure on Symmetric Positive‐Definite Matrices
