A new iterative criterion for H-matrices

H-matrices appear in many areas of science and engineering, e. g., in the solution of the linear complementarity problem (LPC) in optimization theory and in the solution of large systems for real time changes of data in fluid analysis in the car industry. Classical (stationary) iterative methods used for the solution of linear systems have been shown to converge for this class of matrices. Several authors have proposed direct and iterative criteria to identify whether a certain matrix A is an element of C-n,C-n is an H-matrix. Based on previous and new ideas we propose a new iterative algorithm for irreducible matrices A that, except in a "very special" case, decides whether A is an H- or a non H-matrix. A MATLAB subroutine is given and numerical examples are provided in support of the theory developed.