Is A in Cn,n a general H-matrix?

Abstract

H-matrices play an important role in the theory and applications of Numerical Linear Algebra. So, it is very useful to know whether a given matrix A E Cn,n, usually the coefficient of a complex linear system of algebraic equations or of a Linear Complementarity Problem (A E Rn,n, with aii > 0 for i = 1, 2, . . . , n in this case), is an H-matrix; then, most of the classical iterative methods for the solution of the problem at hand converge. In recent years, the set of H-matrices has been extended to what is now known as the set of General H-matrices, and a partition of this set in three different classes has been made. The main objective of this work is to develop an algorithm that will determine the H-matrix character and will identify the class to which a given matrix A E Cn,n belongs; in addition, some results on the classes of general H-matrices and a partition of the non-H-matrix set are presented. © 2011 Elsevier Inc. All rights reserved.