Block LU factorization of M-matrices
Abstract
It is well known that any nonsingular M-matrix admits an LU factorization into M-matrices (with L and U lower and upper triangular respectively) and any singular M-matrix is permutation similar to an M-matrix which admits an LU factorization into M-matrices. Varga and Cai establish necessary and sufficient conditions for a singular M-matrix (without permutation) to allow an LU factorization with L nonsingular. We generalize these results in two directions. First, we find necessary and sufficient conditions for the existence of an LU factorization of a singular M-matrix where L and U are both permitted to be singular. Second, we establish the minimal block structure that a block LU factorization of a singular M-matrix can have when L and U are M-matrices.
Keywords
Cite
@article{arxiv.math/9803098,
title = {Block LU factorization of M-matrices},
author = {Judith J. McDonald and Hans Schneider},
journal= {arXiv preprint arXiv:math/9803098},
year = {2007}
}