The construction of an accurate lower bound for the real parts of the eigenvalues of an M-matrix

AbstractLet A by an M-matrix, i.e., A is nonsingular, real, irreducible, and weakly diagonally dominant and has positive diagonal and nonpositive off-diagonal elements. Via the graph of A we construct a vector W such that AW is positive. This yields a lower bound of the spectrum, which is optimal in certain problems