On the Convergence of a Greedy Rank-One Update Algorithm for a Class of Linear Systems
| hal.structure.identifier | Laboratoire Angevin de Mécanique, Procédés et InnovAtion [LAMPA] | |
| dc.contributor.author | AMMAR, Amine | |
| hal.structure.identifier | Institut de Recherche en Génie Civil et Mécanique [GeM] | |
| dc.contributor.author | CHINESTA, Francisco | |
| hal.structure.identifier | Departamento de Ciencias, Físicas, Matemáticas y de la Computación | |
| dc.contributor.author | FALCO, Antonio | |
| dc.date.accessioned | 2021-05-14T09:52:09Z | |
| dc.date.available | 2021-05-14T09:52:09Z | |
| dc.date.issued | 2010 | |
| dc.identifier.issn | 1134-3060 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/77423 | |
| dc.description.abstractEn | In this paper we study the convergence of the well-known Greedy Rank-One Update Algorithm. It is used to construct the rank-one series solution for full-rank linear systems. The existence of the rank one approximations is also not new, but surprisingly the focus there has been more on the applications side more that in the convergence analysis. Our main contribution is to prove the convergence of the algorithm and also we study the required rank one approximation in each step. We also give some numerical examples and describe its relationship with the Finite Element Method for High-Dimensional Partial Differential Equations based on the tensorial product of one-dimensional bases. We illustrate this situation taking as a model problem the multidimensional Poisson equation with homogeneous Dirichlet boundary condition. | |
| dc.language.iso | en | |
| dc.publisher | Springer Verlag | |
| dc.rights.uri | http://creativecommons.org/licenses/by/ | |
| dc.title.en | On the Convergence of a Greedy Rank-One Update Algorithm for a Class of Linear Systems | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1007/s11831-010-9048-z | |
| dc.subject.hal | Sciences de l'ingénieur [physics]/Mécanique [physics.med-ph] | |
| dc.subject.hal | Sciences de l'ingénieur [physics]/Matériaux | |
| bordeaux.journal | Archives of Computational Methods in Engineering | |
| bordeaux.page | 473-486 | |
| bordeaux.volume | 17 | |
| bordeaux.hal.laboratories | Institut de Mécanique et d’Ingénierie de Bordeaux (I2M) - UMR 5295 | * |
| bordeaux.issue | 4 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.institution | INRAE | |
| bordeaux.institution | Arts et Métiers | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01007145 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01007145v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Archives%20of%20Computational%20Methods%20in%20Engineering&rft.date=2010&rft.volume=17&rft.issue=4&rft.spage=473-486&rft.epage=473-486&rft.eissn=1134-3060&rft.issn=1134-3060&rft.au=AMMAR,%20Amine&CHINESTA,%20Francisco&FALCO,%20Antonio&rft.genre=article |
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