Polynomial roots from companion matrix eigenvalues
Mathematics of Computation
Decomposition of quantics in sums of powers of linear forms
Signal Processing - Special issue on higher order statistics
The Jacobi Method for Real Symmetric Matrices
Journal of the ACM (JACM)
A Multilinear Singular Value Decomposition
SIAM Journal on Matrix Analysis and Applications
On the Best Rank-1 and Rank-(R1,R2,. . .,RN) Approximation of Higher-Order Tensors
SIAM Journal on Matrix Analysis and Applications
Computational Intelligence and Neuroscience - EEG/MEG Signal Processing
Tensor Decompositions and Applications
SIAM Review
Topological features in 2D symmetric higher-order tensor fields
EuroVis'11 Proceedings of the 13th Eurographics / IEEE - VGTC conference on Visualization
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In this paper, we present a sum-of-rank-1 type decomposition and its differential model for symmetric tensors and investigate the convergence properties of numerical gradient-based iterative optimization algorithms to obtain this decomposition. The decomposition we propose reinterprets the orthogonality property of the eigenvectors of symmetric matrices as a geometric constraint on the rank-1 matrix bases, which leads to a geometrically constrained eigenvector frame. Relaxing the orthogonality requirement, we developed a set of structured-bases that can be utilized to decompose any symmetric tensor into a similar constrained sum-of-rank-1 decomposition.