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Towards a Vector Field Based Approach to the Proper Generalized Decomposition (PGD)
dc.contributor.author | Falco, Antonio | |
dc.contributor.author | Hilario Pérez, Lucia | |
dc.contributor.author | Montés, Nicolás | |
dc.contributor.author | Mora, Marta Covadonga | |
dc.contributor.author | Nadal Soriano, Enrique | |
dc.date.accessioned | 2021-02-22T11:41:11Z | |
dc.date.available | 2021-02-22T11:41:11Z | |
dc.date.issued | 2021 | |
dc.identifier.citation | 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 9010034 | ca_CA |
dc.identifier.issn | 2227-7390 | |
dc.identifier.uri | http://hdl.handle.net/10234/192147 | |
dc.description.abstract | 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. | ca_CA |
dc.format.extent | 14 p. | ca_CA |
dc.format.mimetype | application/pdf | ca_CA |
dc.language.iso | eng | ca_CA |
dc.publisher | MDPI | ca_CA |
dc.relation.isPartOf | Mathematics 2021, 9, 34. | ca_CA |
dc.rights | © 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/ licenses/by/4.0/) | ca_CA |
dc.rights | Atribución 4.0 Internacional | * |
dc.rights.uri | http://creativecommons.org/licenses/by-sa/4.0/ | * |
dc.subject | proper generalised decomposition | ca_CA |
dc.subject | alternating least squares | ca_CA |
dc.subject | greedy rank one update algorithm | ca_CA |
dc.subject | tensor numerical methods | ca_CA |
dc.title | Towards a Vector Field Based Approach to the Proper Generalized Decomposition (PGD) | ca_CA |
dc.type | info:eu-repo/semantics/article | ca_CA |
dc.identifier.doi | https://doi.org/10.3390/math9010034 | |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | ca_CA |
dc.relation.publisherVersion | https://www.mdpi.com/2227-7390/9/1/34 | ca_CA |
dc.type.version | info:eu-repo/semantics/publishedVersion | ca_CA |
project.funder.name | Generalitat Valenciana | ca_CA |
project.funder.name | Ministerio de Ciencia, Innovacion y Universidades | ca_CA |
oaire.awardNumber | GVA/2019/124 | ca_CA |
oaire.awardNumber | RTI2018-093521-B-C32 | ca_CA |
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