A new iterative criterion for H-matrices: The reducible case

H-matrices appear in various areas of science and engineering and it is of vital importance to have an Algorithm to identify the H-matrix character of a certain matrix A∈Cn,n. Recently, the present authors have proposed a new iterative criterion (Algorithm AH) to completely identify the H-matrix property of an irreducible matrix. The present work extends the previous Algorithm to cover the reducible case as well.