On the reduction of multivariate quadratic systems to best rank 1 approximation of three way tensors
In this paper, we show that a general quadratic multivariate system in the real field can be reduced to a best rank 1 three way tensor approximation problem. This fact provides a new approach to tackle a system of quadratic polynomials equations. Some experiments using the standard alternating least squares (ALS) algorithm are drawn to evince the usefulness of rank 1 tensor approximation methods.
Appl. Math. Lett.