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dc.contributor.authorMikhalev, Aleksandr
dc.contributor.authorOseledets, I.V.
dc.date.accessioned2017-10-22T11:48:14Z
dc.date.available2017-10-22T11:48:14Z
dc.date.issued2017-10-18
dc.identifier.citationMikhalev A, Oseledets IV (2017) Rectangular maximum-volume submatrices and their applications. Linear Algebra and its Applications. Available: http://dx.doi.org/10.1016/j.laa.2017.10.014.
dc.identifier.issn0024-3795
dc.identifier.doi10.1016/j.laa.2017.10.014
dc.identifier.urihttp://hdl.handle.net/10754/625919
dc.description.abstractWe introduce a definition of the volume of a general rectangular matrix, which is equivalent to an absolute value of the determinant for square matrices. We generalize results of square maximum-volume submatrices to the rectangular case, show a connection of the rectangular volume with an optimal experimental design and provide estimates for a growth of coefficients and an approximation error in spectral and Chebyshev norms. Three promising applications of such submatrices are presented: recommender systems, finding maximal elements in low-rank matrices and preconditioning of overdetermined linear systems. The code is available online.
dc.description.sponsorshipWork on the problem setting and numerical examples was supported by Russian Foundation for Basic Research grant 16-31-60095 mol_a_dk. Work on theoretical estimations of approximation error and the practical algorithm was supported by Russian Foundation for Basic Research grant 16-31-00351 mol_a.
dc.publisherElsevier BV
dc.relation.urlhttp://www.sciencedirect.com/science/article/pii/S0024379517305931
dc.rightsNOTICE: this is the author’s version of a work that was accepted for publication in Linear Algebra and its Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Linear Algebra and its Applications, [, , (2017-10-18)] DOI: 10.1016/j.laa.2017.10.014 . © 2017. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subjectMaximum volume submatrices
dc.subjectPseudo-skeleton approximations
dc.subjectCGR-approximations
dc.subjectRecommender systems
dc.subjectPreconditioning
dc.subjectOptimal experimental design
dc.titleRectangular maximum-volume submatrices and their applications
dc.typeArticle
dc.contributor.departmentExtreme Computing Research Center
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.identifier.journalLinear Algebra and its Applications
dc.eprint.versionPost-print
dc.contributor.institutionInstitute of Numerical Mathematics, Russian Academy of Sciences, Gubkina St. 8, 119333 Moscow, Russia
dc.contributor.institutionSkolkovo Institute of Science and Technology, Novaya St. 100, Skolkovo, Odintsovsky district, 143025, Russia
dc.identifier.arxivid1502.07838
kaust.personMikhalev, Aleksandr
refterms.dateFOA2019-10-18T00:00:00Z
dc.date.published-online2017-10-18
dc.date.published-print2018-02


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