Maximum-volume principle for rectangular matrices


A definition of p-volume of rectangular matrices is given. We generalize the results for square maximum-volume submatrices to the case rectangular maximal-volume submatrices and provide estimates for the growth of the coefficients. Three promising applications of such submatrices are presented: recommender systems, finding maximal elements in low-rank matrices and preconditioning of overdetermined linear systems.


26/05/2016 A TT-eigenvalue solver that finally works
12/05/2016 Exponential machines and tensor trains
06/04/2016 Convergence analysis of a projected fixed-point iteration
30/03/2016 Compress-and-eliminate solver for sparse matrices
01/12/2015 New paper in SIMAX


We are located at the 2-nd floor of the new "Technopark-3” building in Skolkovo (few kilometers outside Moscow Ring Road). The building is accessible from Skolkovo Road (Сколковское шоссе) and Minskoe Highway (Минское шоссе).