ELLIPTIC DICHOTOMY OF A MATRIX SPECTRUM

Given a regular linear matrix pencil lambda A + B and an ellipse Gamma in the complex plane, we describe an algorithm for computing the righ t invariant subspaces of lambda A + B associated to the eigenvalues in side and outside the ellipse. The algorithm builds a particular matrix pencil of order twice the order of the pencil lambda A + B, to which circular dichotomy techniques can be applied efficiently. The algorith m allows also the computation of the canonical form of the pencil lamb da A + B.