Falcó Montesinos, AntonioMora Aguilar, Marta CovadongaNadal Soriano, EnriqueHilario Pérez, LucíaMontés Sánchez, NicolásProducción Científica UCH 2021UCH. Departamento de Matemáticas, Física y Ciencias Tecnológicas2021-07-172021-07-172021-01-01Falcó, A., Hilario, L., Montés, N., Mora, M.C. & Nadal, E. (2021). Towards a vector field based approach to the Proper Generalized Decomposition (PGD). Mathematics, vol. 9, i. 1 (25 dec.), art. 34. DOI: https://doi.org/10.3390/math90100342227-7390 (Electrónico).http://hdl.handle.net/10637/12883Este artículo se encuentra disponible en la siguiente URL: https://www.mdpi.com/2227-7390/9/1/34Este artículo pertenece al número especial "Applications of partial differential equations in Engineering".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 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 rank-one optimization problem. To obtain this result, we endow the set of tensors with fixed rank-one with an explicit geometric structure.application/pdfesopen accessAlgoritmos.Algorithms.Álgebra de tensores.Descomposición (Matemáticas)Ecuaciones en derivadas parciales.Differential equations, Partial.Decomposition (Mathematics)Tensor algebra.Artículohttps://doi.org/10.3390/math9010034https://creativecommons.org/licenses/by-nc-nd/4.0/deed.es