Inequalities for M-matrices and inverse M-matrices

Two modified Jacobi methods for M-matrices

M-matrices Satisfy Newton’s Inequalities

Newton’s inequalities cn ≥ cn−1cn+1 are shown to hold for the normalized coefficients cn of the characteristic polynomial of any Mor inverse M-matrix. They are derived by establishing first an auxiliary set of inequalities also valid for both of these classes. They are also used to derive some new necessary conditions on the eigenvalues of nonnegative matrices.

Hadamard Functions of Inverse M-Matrices

We prove that the class of GUM matrices is the largest class of bi-potential matrices stable under Hadamard increasing functions. We also show that any power α ≥ 1, in the sense of Hadamard functions, of an inverseM -matrix is also inverseM matrix showing a conjecture stated in Neumann [15]. We study the class of filtered matrices, which include naturally the GUM matrices, and present some suff...

Ela a Note on Newton and Newton–like Inequalities for M–matrices and for Drazin Inverses of M–matrices∗

In a recent paper Holtz showed that M–matrices satisfy Newton’s inequalities and so do the inverses of nonsingular M–matrices. Since nonsingular M–matrices and their inverses display various types of monotonic behavior, monotonicity properties adapted for Newton’s inequalities are examined for nonsingular M–matrices and their inverses. In the second part of the paper the problem of whether Draz...

two modified jacobi methods for m-matrices