Eigenvectors of tensors and algorithms for Waring decomposition

Abstract

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 equation of certain secant varieties and to eigenvectors of tensors. In particular we explicitly decompose a general cubic polynomial in three variables as the sum of five cubes (Sylvester Pentahedral Theorem).

32 pages; three Macaulay2 files as ancillary files. Revised with referee's suggestions. Accepted JSC

References in corpus (4)

• The Number of Eigenvalues of a Tensor
• Decomposition of homogeneous polynomials with low rank
• Equations for secant varieties to Veronese varieties
• Secant varieties of P^2 x P^n embedded by O(1,2)

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