Towards a Vector Field Based Approach to the Proper Generalized Decomposition (PGD)
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Título
Towards a Vector Field Based Approach to the Proper Generalized Decomposition (PGD)Autoría
Fecha de publicación
2021Editor
MDPIISSN
2227-7390Cita bibliográfica
Falcó, A.; Hilario, L.; Montés, N.; Marta, M.C.; Nadal, E. Towards a Vector Field Based Approach to the Proper Generalized Decomposition (PGD). Mathematics 2021, 9, 34. https://dx.doi.org/10.3390/math 9010034Tipo de documento
info:eu-repo/semantics/articleVersión de la editorial
https://www.mdpi.com/2227-7390/9/1/34Versión
info:eu-repo/semantics/publishedVersionPalabras clave / Materias
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 ... [+]
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. [-]
Publicado en
Mathematics 2021, 9, 34.Entidad financiadora
Generalitat Valenciana | Ministerio de Ciencia, Innovacion y Universidades
Código del proyecto o subvención
GVA/2019/124 | RTI2018-093521-B-C32
Derechos de acceso
info:eu-repo/semantics/openAccess
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