Iterative Methods for Linear Complementarity Problems with Interval Data

In this paper we introduee the total step method, the single step method and the symmetrie single step method for linear eomplementarity problems with interval data. They are applied to an interval matrix [A] and an interval veetor [b]. If all A E [A] are H-matrices with positive diagonal elements, these methods are all eonvergent to the same interval veetor [x*].This interval vector indudes the solution x of the linear complementarity problem defined by any fixed A E [A]and any fixed b E [b].If all A E [A] are M-matrices, then we will show, that [x*]is optimal in a precisely defined sense. We also consider modifications of those methods, whieh under eertain assumptions on the starting vector deliver nested sequences converging to [x*].We dose our paper with some examples which illustrate our theoretical results