] 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.