New accelerated modulus-based iteration method for solving large and sparse linear complementarity problem

Abstract

For the large and sparse linear complementarity problem, we provide a family of new accelerated modulus-based iteration methods in this article. We provide some sufficient criteria for the convergence analysis when the system matrix is a \(P\)-matrix or an \(H_+\)-matrix. In addition, we provide some numerical examples of the different parameters to illustrate the efficacy of our proposed methods. These methods help us reduce the number of iterations and the time required by the CPU, which improves convergence performance.

Keywords

• Linear complementarity problem
• $P$-matrix
• $H_{ }$-matrix
• matrix splitting
• convergence