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dc.contributor.author | Falco, Antonio | es_ES |
dc.contributor.author | Hilario Pérez, Lucia | es_ES |
dc.contributor.author | Montés Sánchez, Nicolás | es_ES |
dc.contributor.author | Mora Aguilar, Marta Covadonga | es_ES |
dc.contributor.author | Nadal, Enrique | es_ES |
dc.date.accessioned | 2021-11-05T14:11:18Z | |
dc.date.available | 2021-11-05T14:11:18Z | |
dc.date.issued | 2021-01 | es_ES |
dc.identifier.uri | http://hdl.handle.net/10251/176451 | |
dc.description.abstract | [EN] 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 | es_ES |
dc.description.sponsorship | This research was funded by the GVA/2019/124 grant from Generalitat Valenciana and by the RTI2018-093521-B-C32 grant from the Ministerio de Ciencia, Innovacion y Universidades. Document | es_ES |
dc.language | Inglés | es_ES |
dc.publisher | MDPI AG | es_ES |
dc.relation.ispartof | Mathematics | es_ES |
dc.rights | Reconocimiento (by) | es_ES |
dc.subject | Proper generalised decomposition | es_ES |
dc.subject | Alternating least squares | es_ES |
dc.subject | Greedy rank one update algorithm | es_ES |
dc.subject | Tensor numerical methods | es_ES |
dc.subject.classification | INGENIERIA DE SISTEMAS Y AUTOMATICA | es_ES |
dc.subject.classification | INGENIERIA MECANICA | es_ES |
dc.title | Towards a Vector Field Based Approach to the Proper Generalized Decomposition (PGD) | es_ES |
dc.type | Artículo | es_ES |
dc.identifier.doi | 10.3390/math9010034 | es_ES |
dc.relation.projectID | info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/RTI2018-093521-B-C32/ES/GEOMETRIA Y TOPOLOGIA DE LOS MODELOS DE ORDEN REDUCIDO: APLICACIONES EN ARQUITECTURA/ | es_ES |
dc.relation.projectID | info:eu-repo/grantAgreement/GVA//GVA%2F2019%2F124/ | es_ES |
dc.rights.accessRights | Abierto | es_ES |
dc.contributor.affiliation | Universitat Politècnica de València. Departamento de Ingeniería Mecánica y de Materiales - Departament d'Enginyeria Mecànica i de Materials | es_ES |
dc.contributor.affiliation | Universitat Politècnica de València. Departamento de Ingeniería de Sistemas y Automática - Departament d'Enginyeria de Sistemes i Automàtica | es_ES |
dc.contributor.affiliation | Universitat Politècnica de València. Instituto de Diseño para la Fabricación y Producción Automatizada - Institut de Disseny per a la Fabricació i Producció Automatitzada | es_ES |
dc.description.bibliographicCitation | Falco, A.; Hilario Pérez, L.; Montés Sánchez, N.; Mora Aguilar, MC.; Nadal, E. (2021). Towards a Vector Field Based Approach to the Proper Generalized Decomposition (PGD). Mathematics. 9(1):1-14. https://doi.org/10.3390/math9010034 | es_ES |
dc.description.accrualMethod | S | es_ES |
dc.relation.publisherversion | https://doi.org/10.3390/math9010034 | es_ES |
dc.description.upvformatpinicio | 1 | es_ES |
dc.description.upvformatpfin | 14 | es_ES |
dc.type.version | info:eu-repo/semantics/publishedVersion | es_ES |
dc.description.volume | 9 | es_ES |
dc.description.issue | 1 | es_ES |
dc.identifier.eissn | 2227-7390 | es_ES |
dc.relation.pasarela | S\424621 | es_ES |
dc.contributor.funder | Generalitat Valenciana | es_ES |
dc.contributor.funder | Agencia Estatal de Investigación | es_ES |