Accelerated double-relaxation modulus-based matrix splitting iteration method for linear complementarity problems

Abstract

This paper is concerned with solving linear complementarity problems (LCP) arising in many scientific and engineering fields. We propose an accelerated double-relaxation two-sweep modulus-based matrix splitting (ADRTMMS) iteration method by applying accelerating, relaxation and relaxation two-sweep techniques to the MMS one. This new method contains some known ones developed recently. Some sufficient conditions for guaranteeing the convergence of the ADRTMMS method are presented when the system matrices both are positive definite matrices and H+-matrices, which generalize some existing results. Specially, the convergence of the ADRTM accelerated overrelaxation (ADRTMAOR) method is discussed in details. At last, some numerical examples are provided to show that the ADRTMMS method is efficient and outperforms several existing MMS-like methods.

Keywords

• Linear complementarity problems
• Modulus-based matrix splitting iteration method
• Relaxation technique
• Relaxation two-sweep strategy
• Accelerated double-relaxation
• Convergence