A PLU-factorization of rectangular matrices by the Neville elimination Original Research Article

In this paper we prove that Neville elimination can be matricially described by elementary matrices. A PLU-factorization is obtained for any n×m matrix, where P is a permutation matrix, L is a lower triangular matrix (product of bidiagonal factors) and U is an upper triangular matrix. This result generalizes the Neville factorization usually applied to characterize the totally positive matrices. We prove that this elimination procedure is an alternative to Gaussian elimination and sometimes provides a lower computational cost.