Modulus-Based GSTS Iteration Method for Linear Complementarity Problems (Journal of Mathematical Study, 2018)
In this paper, a modulus-based generalized skew-Hermitian triangular splitting(MGSTS) iteration method is present for solving a class of linear complementarityproblems with the system matrix either being an $H_+$-matrix with non-positiveoff-diagonal entries or a symmetric positive definite matrix. The convergence of theMGSTS iteration method is studied in detail. By choosing different parameters, a seriesof existing and new iterative methods are derived, including the modulus-based Jacobi(MJ) and the modulus-based Gauss-Seidel (MGS) iteration methods and so on. Experimentalresults are given to show the effectiveness and feasibility of the new methodwhen it is employed for solving this class of linear complementarity problems.
Keywords: GSTS method; modulus-based iteration method; linear complementarity problem; $H_+$-matrix; symmetric positive definite matrix.