KAUST DepartmentExtreme Computing Research Center
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
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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.
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.
SponsorsWork 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.