An extended compact profile iterative method criterion for sparse H-matrices Original Research Article

In the theory and applications of Numerical Linear Algebra the class of H-matrices is very important. For example, when one is interested in the solution of linear systems of algebraic equations and their solution is sought by classical iterative methods (e.g., Jacobi, Gauss–Seidel, SOR, SSOR, etc.). In recent years many works have appeared that propose criteria for a matrix image to be an H-matrix (see, e.g. [Linear Algebra Appl. 374 (2003) 317; Linear Algebra Appl. 169 (1992) 257; Linear Algebra Appl. 248 (1996) 339; Int. J. Comput. Math. 60 (1996) 115; J. Comput. Appl. Math. 115 (1995) 237; J. Comput. Appl. Math. 115 (2000) 349; Linear Algebra Appl. 271 (1998) 179; J. Comput. Appl. Math. 150 (2003) 293]). In the present work we propose one more such a criterion together with an algorithm. As far as we know it is the first time the zero pattern of A, which in practical problems is usually large and sparse, is taken into consideration. As a consequence both storage and number of operations required to decide about the H-character of the matrix A are drastically reduced. Finally, we use our method with a set of numerical examples to show its effectiveness.