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Título : Towards a vector field based approach to the Proper Generalized Decomposition (PGD)
Autor : Falcó Montesinos, Antonio.
Hilario Pérez, Lucía.
Montés Sánchez, Nicolás.
Mora Aguilar, Marta Covadonga.
Nadal Soriano, Enrique.
Materias: Algoritmos.Algorithms.Álgebra de tensores.Descomposición (Matemáticas)Ecuaciones en derivadas parciales.Differential equations, Partial.Decomposition (Mathematics)Tensor algebra.
Fecha de publicación : 1-ene-2021
Editorial : MDPI.
Citación : Falcó, 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/math9010034
Resumen : 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.
Descripción : Este artículo se encuentra disponible en la siguiente URL: https://www.mdpi.com/2227-7390/9/1/34
Este artículo pertenece al número especial "Applications of partial differential equations in Engineering".
URI : http://hdl.handle.net/10637/12883
Derechos: http://creativecommons.org/licenses/by/4.0/deed.es
ISSN : 2227-7390 (Electrónico).
Aparece en las colecciones: Dpto. Matemáticas, Física y Ciencias Tecnológicas

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