Eigenvectors of tensors and algorithms for Waring decomposition
Luke Oeding
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. Landsberg and Ottaviani recently gave
a new class of equations for secant varieties based on vector bundle
techniques. The presentation of these equations has the advantage
that it can also be used to compute a Waring decomposition. Our
algorithms use these equations and the concept of an eigenvector of a
tensor. I will discuss the construction of the Landsberg-Ottavian
equations, introduce the notion of an eigenvector of a tensor, and
show our algorithms in practice.
In particular I will show how we explicitly decompose a general cubic
polynomial in three variables as the sum of five cubes (Sylvester
Pentahedral Theorem).