Iterative methods with analytical preconditioning technique to linear complementarity problems: application to obstacle problems

¹ Department of Mathematics, Faculty of Sciences, Islamic Azad University, Lahijan Branch, Iran
hnajafi@guilan.ac.ir
² Young Researchers Club, Lahijan Branch, Islamic Azad University, Lahijan, Iran
saedalatpanah@gmail.com

Received: 29 February 2012
Accepted: 3 December 2012

Abstract

For solving linear complementarity problems LCP more attention has recently been paid on a class of iterative methods called the matrix-splitting. But up to now, no paper has discussed the effect of preconditioning technique for matrix-splitting methods in LCP. So, this paper is planning to fill in this gap and we use a class of preconditioners with generalized Accelerated Overrelaxation (GAOR) methods and analyze the convergence of these methods for LCP. Furthermore, Comparison between our methods and other non-preconditioned methods for the studied problem shows a remarkable agreement and reveals that our models are superior in point of view of convergence rate and computing efficiency. Besides, by choosing the appropriate parameters of these methods, we derive same results as the other iterative methods such as AOR, JOR, SOR etc. Finally the method is tested by some numerical experiments.