# IJPAM: Volume 28, No. 1 (2006)

**AN ITERATIVE ALGORITHM FOR THE LINEAR**

COMPLEMENTARITY PROBLEM WITH AN -MATRIX

COMPLEMENTARITY PROBLEM WITH AN -MATRIX

Lei Li, Yushi Sato

Faculty of Engineering

Hosei University

Koganei, Tokyo, 184-8584, JAPAN

e-mail: lilei@k.hosei.ac.jp

Faculty of Engineering

Hosei University

Koganei, Tokyo, 184-8584, JAPAN

e-mail: lilei@k.hosei.ac.jp

**Abstract.**It is well known that the linear complementarity problem LCP(, ) which consists of finding a vector
such that

where and are a given real matrix and a real vector, respectively. We have proposed an direct recursive algorithm when is an -matrix [#!1!#]. In [#!2!#], a block version of the algorithm was considered. Many numerical examples are showing that the block version takes fewer number of the arithmetic operations than the non-block version. In this paper, we propose a kind of splitting algorithms for solving LCP(, ), where is an -matrix. The main idea of the algorithm is to devide the -matrix into an -matrix and a nonnegative matrix, and to solve an LCP with the -matrix as subproblems. Some numerical examples are shown.

**Received: **April 15, 2006

**AMS Subject Classification: **90C33

**Key Words and Phrases: **linear complementarity problem, -matrix, iterative algorithm

**Source:** International Journal of Pure and Applied Mathematics

**ISSN:** 1311-8080

**Year:** 2006

**Volume:** 28

**Issue:** 1