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Abstract: For many applications, it is useful to know whether or not a matrix is an H-matrix. An algorithmic characterization of H-matrices was given by [Li et al.] This method is useful, but entails estimating an optimum value for a parameter ε, that plays a crucial role in the algorithm. In Part I of this paper, the authors present a new method which eliminates the arbitrary parameter and is an equivalent algorithmic characterization of H-matrices. A few examples are given to illustrate relative merits of the two methods. In Part II, the editor describes an alternative which seems to eliminate deficiencies in methods discussed in Part I. [Copyright &y& Elsevier]