A class of modified modulus-based synchronous multisplitting iteration methods for linear complementarity problems

In this paper, we present modified modulus-based synchronous multisplitting iteration methods based on multisplittings of the system matrix for solving the large sparse linear complementarity problems. The proposed methods extend the existing modulus-based synchronous multisplitting iteration methods to a more general case. We establish the convergence theory of these modified modulus-based synchronous multisplitting iteration methods when the system matrix is an H + -matrix. In particular, we investigate the optimal choice of the parameter matrices in theory. Numerical results confirm that the new iteration methods have higher parallel computational efficiency than the existing modulus-based synchronous multisplitting iteration methods. The proposed methods are applied in reconstruction of two-dimensional image data and show the efficiency.