Decomposition of quantics in sums of powers of linear forms
Signal Processing - Special issue on higher order statistics
Tensor Rank and the Ill-Posedness of the Best Low-Rank Approximation Problem
SIAM Journal on Matrix Analysis and Applications
Eigenvalues of a real supersymmetric tensor
Journal of Symbolic Computation
Computing symmetric rank for symmetric tensors
Journal of Symbolic Computation
Foundations of Computational Mathematics
Efficiently Computing Tensor Eigenvalues on a GPU
IPDPSW '11 Proceedings of the 2011 IEEE International Symposium on Parallel and Distributed Processing Workshops and PhD Forum
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A Waring decomposition of a (homogeneous) polynomial f is a minimal sum of powers of linear forms expressing f. Under certain conditions, such a decomposition is unique. We discuss some algorithms to compute the Waring decomposition, which are linked to the equations of certain secant varieties and to eigenvectors of tensors. In particular we explicitly decompose a cubic polynomial in three variables as the sum of five cubes (Sylvester Pentahedral Theorem).