Convergence analysis of projected SOR iteration method for a class of vertical linear complementarity problems

Based on the ideas of the projected matrix splitting technique and the well-known successive overrelaxation (SOR) iteration method, a projected SOR (PSOR) iteration method is studied in this paper for solving a class of vertical linear complementarity problems, where the system matrix is a vertical block matrix of several square sub-blocks with positive diagonal elements. Convergence analyses of the PSOR iteration method are carefully studied when the square sub-blocks and their row-representative matrices are strictly diagonally dominant, irreducibly diagonally dominant and H+-matrices, respectively. At last, two numerical examples are presented. Numerical results indicate that the PSOR method performs much better than some recent proposed projected splitting methods.