dc.creator | Azaïez, Mejdi | es |
dc.creator | Lestandi, Lucas | es |
dc.creator | Chacón Rebollo, Tomás | es |
dc.date.accessioned | 2019-10-07T07:20:38Z | |
dc.date.available | 2019-10-07T07:20:38Z | |
dc.date.issued | 2019 | |
dc.identifier.citation | Azaïez, M., Lestandi, L., y Chacón Rebollo, T. (2019). Low rank approximation of multidimensional data. En High-performance computing of big data for turbulence and combustion (pp. 187-250). Cham: Springer | |
dc.identifier.isbn | 9783030170110 | es |
dc.identifier.isbn | 9783030170127 | es |
dc.identifier.uri | https://hdl.handle.net/11441/89456 | |
dc.description.abstract | In the last decades, numerical simulation has experienced tremendous improvements driven by massive growth of computing power. Exascale computing has been achieved this year and will allow solving ever more complex problems. But such large systems produce colossal amounts of data which leads to its own difficulties. Moreover, many engineering problems such as multiphysics or optimisation and control, require far more power that any computer architecture could achieve within the current scientific computing paradigm. In this chapter, we propose to shift the paradigm in order to break the curse of dimensionality by introducing decomposition to reduced data. We present an extended review of data reduction techniques and intends to bridge between applied mathematics
community and the computational mechanics one. The chapter is organized into two parts. In the first one bivariate separation is studied, including discussions on the equivalence of proper orthogonal decomposition (POD, continuous framework) and singular value decomposition (SVD, discrete matrices). Then, in the second part, a wide review of tensor formats and their approximation is proposed. Such work has already been provided in
the literature but either on separate papers or into a pure applied
mathematics framework. Here, we offer to the data enthusiast scientist a description of Canonical, Tucker, Hierarchical and Tensor train formats including their approximation algorithms. When it is possible, a careful analysis of the link between continuous and discrete methods will be performed. | es |
dc.description.sponsorship | IV Research and Transfer Plan of the University of Sevilla | es |
dc.description.sponsorship | Institut Carnot | es |
dc.description.sponsorship | Junta de Andalucía | es |
dc.description.sponsorship | IDEX program of the University of Bordeaux | es |
dc.format | application/pdf | es |
dc.language.iso | eng | es |
dc.publisher | Springer | es |
dc.relation.ispartof | High-performance computing of big data for turbulence and combustion | es |
dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 Internacional | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | * |
dc.subject | Data reduction | es |
dc.subject | Model reduction | es |
dc.subject | Singular values decomposition | es |
dc.subject | Data | es |
dc.subject | MOR | es |
dc.subject | POD | es |
dc.subject | HOSVD | es |
dc.subject | Low rank approximation | es |
dc.subject | Tensors | es |
dc.subject | Tensor train | es |
dc.title | Low rank approximation of multidimensional data | es |
dc.type | info:eu-repo/semantics/bookPart | es |
dcterms.identifier | https://ror.org/03yxnpp24 | |
dc.type.version | info:eu-repo/semantics/submittedVersion | es |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | es |
dc.contributor.affiliation | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico | es |
dc.relation.projectID | FQM 454 | es |
dc.relation.publisherversion | https://link.springer.com/chapter/10.1007/978-3-030-17012-7_5 | es |
dc.identifier.doi | https://doi.org/10.1007/978-3-030-17012-7_5 | es |
dc.contributor.group | Universidad de Sevilla. FQM120: Modelado Matemático y Simulación de Sistemas Medioambientales | es |
idus.format.extent | 69 p. | es |
dc.publication.initialPage | 187 | es |
dc.publication.endPage | 250 | es |
dc.relation.publicationplace | Cham | es |