General double-relaxation two-sweep modulus-based matrix splitting iteration methods for horizontal linear complementarity problem

For solving horizontal linear complementarity problem (HLCP), we propose a general double-relaxation two-sweep modulus-based matrix splitting iteration method and a double-relaxation two-sweep modulus-based matrix splitting iteration method which contain a series of methods, by using different splittings. When the system matrices are \(H_+\) $H_{+}$ -matrices, we analyze convergence theory of these methods. Numerical examples in this paper illustrate that these methods are more efficient than modulus-based matrix splitting iteration method and general modulus-based matrix splitting iteration method.