Iterative methods for linear complementarity problems with interval data

  • Authors:

  • G. Alefeld;U. Schäfer

  • Affiliations:

  • Institut für Angewandte Mathematik, Kaiserstrasse 12, D-76128 Karlsruhe, Germany;Institut für Angewandte Mathematik, Kaiserstrasse 12, D-76128 Karlsruhe, Germany

  • Venue:
  • Computing
  • Year:
  • 2003

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Abstract

In this paper we introduce the total step method, the single step method and the symmetric single step method for linear complementarity problems with interval data. They are applied to an interval matrix [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.