An alternative to the Ritz pairs with the EN subspace method

In this note we define EN subspaces by using the Eirola-Nevanlinna algorithm for solving a linear system. We compare this construction with the Arnoldi method for generating Krylov subspaces and computing eigenvalue approximations. Further, we compute Ritz pairs by restricting the updated preconditionerH _k of the EN algorithm to the generated EN subspaces.