On the computation of all eigenvalues for the eigenvalue complementarity problem

In this paper, a parametric algorithm is introduced for computing all eigenvalues for two Eigenvalue Complementarity Problems discussed in the literature. The algorithm searches a finite number of nested intervals [ ?̄?, ?̄?] in such a way that, in each iteration, either an eigenvalue is computed in [?̄?, ?̄?] or a certificate of nonexistence of an eigenvalue in [ ?̄?, ?̄?] is provided. A hybrid method that combines an enumerative method [5] and a semi-smooth algorithm [1] is discussed for dealing with the Eigenvalue Complementarity Problem over an interval [ ?̄?, ?̄?]. Computational experience is presented to illustrate the efficacy and efficiency of the proposed techniques.