Volume-based subset selection

This paper provides a fast algorithm for the search of a dominant (locally maximum volume) submatrix, generalizing the existing algorithms from n ? r to n > r submatrix columns, where r is the number of searched rows. We prove the bound on the number of steps of the algorithm, which allows it to outper-form the existing subset selection algorithms in either the bounds on the norm of the pseudoinverse of the found submatrix, or the bounds on the complexity, or both.