Is \(A\in\mathbb C^{n,n}\) a general \(H\)-matrix? (Q651209)

The aim of the paper is to develop an algorithm that determines the \(H\)-matrix character and identifies the class to which a given matrix \(A\in\mathbf C^{n,n}\) belongs. The first section is an introduction in nature. The second section presents the basic notation and definitions, and the required background material is presented. Also, some new results on classes of \(H\)- and non-\(H\)-matrices are summarized. The two parts of the third section develop the IRR algorithm, whose purpose is to determine the irreducible character of a square complex matrix. In the fourth section, based on the previous results the authors present the complete algorithm to determine the irreducible/reducible character as well the \(H\)-/non-\(H\)-matrix character and the class of a general matrix \(A\in\mathbf C^{n,n}\). In order to support the theory, the fifth section gives some numerical examples that cover all six mutually exclusive classes of \(H\)-/non-\(H\)-matrices.