A relaxation accelerated two-sweep modulus-based matrix splitting iteration method for solving linear complementarity problems

TL;DR

This paper introduces a relaxation accelerated two-sweep matrix splitting iteration method for solving linear complementarity problems, demonstrating improved efficiency and convergence under specific matrix conditions.

Contribution

The paper proposes a novel relaxation accelerated two-sweep matrix splitting method with proven convergence for $H_+$-matrix systems, enhancing solution efficiency.

Findings

Method converges to exact solution for $H_+$-matrix systems.

Numerical experiments show improved efficiency over existing methods.

Convergence conditions are explicitly provided.

Abstract

For a linear complementarity problem, we present a relaxaiton accelerated two-sweep matrix splitting iteration method. The convergence analysis illustrates that the proposed method converges to the exact solution of the linear complementarity problem when the system matrix is an $H_+$-matrix and the convergence conditions are given. Numerical experiments show that the proposed method is more efficient than the existing ones.