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$$ n\leqslant r $$ to n>r$$ n>r $$ submatrix columns, where r$$ r $$ is the number of searched rows. We prove the bound on the number of steps of the algorithm, which allows it to outperform 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.