Journal of Mathematical Sciences and Applications. 2013, 1(1), 6-11DOI:
Abstract: The Linear Complementarity Problem LCP(M,q) is to find a vector x in IRn satisfying x≥0, Mx+q≥0 and xT(Mx+q)=0, where M as a matrix and q as a vector, are given data. In this paper we show that the linear complementarity problem is completely equivalent to finding the fixed point of the map x = max (0, (I-M)x-q); to find an approximation solution to the second problem, we propose an algorithm starting from any interval vector X(0) and generating a sequence of the interval vector (X(k))k=1 which converges to the exact solution of our linear complementarity problem. We close our paper with some examples which illustrate our theoretical results.