The solution of the linear complementarity problem by the matrix analogue of the accelerated overrelaxation iterative method

The Linear Complementarity Problem (LCP), with an H+−matrix coefficient, is solved by using the new “(Projected) Matrix Analogue of the AOR (MAAOR)” iterative method; this new method constitutes an extension of the “Generalized AOR (GAOR)” iterative method. In this work two sets of convergence intervals of the parameters involved are determined by the theories of “Perron-Frobenius” and of “Regular Splittings”. It is shown that the intervals in question are better than any similar convergence intervals found so far by similar iterative methods. A deeper analysis reveals that the “best” values of the parameters involved are those of the (projected) scalar Gauss-Seidel iterative method. A theoretical comparison of the “best” (projected) Gauss-Seidel and the “best” modulus-based splitting Gauss-Seidel method is in favor of the former method. A number of numerical examples support most of our theoretical findings.

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