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    Rectangular maximum-volume submatrices and their applications

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    1-s2.0-S0024379517305931-main.pdf
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    Description:
    Accepted Manuscript
    Embargo End Date:
    2019-10-18
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    Type
    Article
    Authors
    Mikhalev, Aleksandr
    Oseledets, I.V.
    KAUST Department
    Extreme Computing Research Center
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Date
    2017-10-18
    Permanent link to this record
    http://hdl.handle.net/10754/625919
    
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    Abstract
    We 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.
    Citation
    Mikhalev 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.
    Sponsors
    Work 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.
    Publisher
    Elsevier BV
    Journal
    Linear Algebra and its Applications
    ISSN
    0024-3795
    DOI
    10.1016/j.laa.2017.10.014
    Additional Links
    http://www.sciencedirect.com/science/article/pii/S0024379517305931
    ae974a485f413a2113503eed53cd6c53
    10.1016/j.laa.2017.10.014
    Scopus Count
    Collections
    Articles; Extreme Computing Research Center; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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