Modulus-based matrix splitting iteration methods for linear complementarity problems

For the large sparse linear complementarity problems, by reformulating them as implicit fixed-point equations based on splittings of the system matrices, we establish a class of modulus-based matrix splitting iteration methods and prove their convergence when the system matrices are positive-definite matrices and H+-matrices. These results naturally present convergence conditions for the symmetric positive-definite matrices and the M-matrices. Numerical results show that the modulus-based relaxation methods are superior to the projected relaxation methods as well as the modified modulus method in computing efficiency.