Iterative Methods for Linear Complementarity Problems with Interval Data

A ] and an interval vector [b]. If all A∈[A] are H-matrices with positive diagonal elements, these methods are all convergent to the same interval vector [x ^*]. This interval vector includes the solution x of the linear complementarity problem defined by any fixed A∈[A] and any fixed b∈[b]. If all A∈[A] are M-matrices, then we will show, that [x ^*] is optimal in a precisely defined sense. We also consider modifications of those methods, which under certain assumptions on the starting vector deliver nested sequences converging to [x ^*]. We close our paper with some examples which illustrate our theoretical results. Received October 7, 2002; revised April 15, 2003 Published online: June 23, 2003 RID="*" ID="*" Dedicated to U. Kulisch on the occasion of his 70th birthday. We are grateful to the referee who has given a series of valuable comments.