A novel algorithm called the Proper Generalized Decomposition (PGD) is widely used by the engineering community to compute the solution of high dimensional problems.However, it is well-known that sweet life carts the bottleneck of its practical implementation focuses on the computation of the so-called best rank-one approximation.Motivated by this fact, we are going to discuss some of the geometrical aspects of the best rank-one approximation procedure.
More precisely, our main result is to construct explicitly a vector field over a low-dimensional vector space and to prove that we can identify its stationary points with the critical points of the best hand wipes individual packets rank-one optimization problem.To obtain this result, we endow the set of tensors with fixed rank-one with an explicit geometric structure.