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Embargo End Date:
2019-10-18
Type
ArticleKAUST Department
Extreme Computing Research CenterComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Date
2017-10-18Permanent link to this record
http://hdl.handle.net/10754/625919
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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 BVISSN
0024-3795Additional Links
http://www.sciencedirect.com/science/article/pii/S0024379517305931ae974a485f413a2113503eed53cd6c53
10.1016/j.laa.2017.10.014