Towards a Vector Field Based Approach to the Proper Generalized Decomposition (PGD)

Towards a Vector Field Based Approach to the Proper Generalized Decomposition (PGD)

Blog Article

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, Arm Chair with Cushion (set of 2) it is well-known that 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 SWEET 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 rank-one optimization problem.To obtain this result, we endow the set of tensors with fixed rank-one with an explicit geometric structure.