Weighted max-norm estimate of two-stage splitting method for solving a class of nonlinear complementarity problems

Abstract

In this paper, we consider the splitting method and the two-stage splitting method for solving a class of nonlinear complementarity problems with the coefficient matrix being an $$H$$ H -matrix. Convergence result for the splitting method is presented when the splitting is $$H$$ H -splitting. Moreover, for the two-stage splitting method, we estimate weighted max-norm bounds for iteration errors, and thereby, we show that the sequence generated by the two-stage iteration scheme converges to the unique solution of the nonlinear complementarity problem without any restriction on the initial vector. Numerical results show that both methods are efficient for solving the class of nonlinear complementarity problems.