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 \(\bar{l}, \bar{u}]\) in such a way that, in each iteration, either an eigenvalue is computed in \(\bar{l}, \bar{u}]\) or a certificate of nonexistence of an eigenvalue in \(\bar{l}, \bar{u}]\) is provided. A hybrid method that combines an enumerative method 1] and a semi-smooth algorithm 2] is discussed for dealing with the Eigenvalue Complementarity Problem over an interval \(\bar{l}, \bar{u}]\) . Computational experience is presented to illustrate the efficacy and efficiency of the proposed techniques.