On iterative criteria for H- and non-H-matrices

The identification of the H-matrix property of the coefficient matrix of a linear system of equations is of great theoretical and practical importance since H-matrices have many applications in science and engineering. For this identification many direct and iterative criteria already exist. In this article we present new iterative criteria which are proved to be faster than similar previous ones for the desired identification; these criteria may also take advantage of a possible sparsity of the matrix. Together with the algorithms that are proposed various illustrative numerical examples are provided.