On nonsingular \(M\)-matrices (Q1316170)

The authors extend the result for a nonsingular irreducible \(M\)-matrix to a nonsingular \(M\)-matrix, i.e. they prove that for a nonsingular \(M\)- matrix \(S\) and vectors \(x\) and \(y\) such that \(Sx=y\) and \(y_ K \neq 0\) for each nucleus \(K\) and \(x_ i>0\) whenever \(y_ i<0\), then \(x \gg 0\). As application the bounds of solutions and their relative errors are discussed.