Elliptic dichotomy of a matrix spectrum Original Research Article

Given a regular linear matrix pencil λA + B and an ellipse Γ in the complex plane, we describe an algorithm for computing the right invariant subspaces of λA + B associated to the eigenvalues inside and outside the ellipse. The algorithm builds a particular matrix pencil of order twice the order of the pencil λA + B, to which circular dichotomy techniques can be applied efficiently. The algorithm allows also the computation of the canonical form of the pencil λA + B.