Spectral refinement for clustered eigenvalues of quasi-diagonal matrices

We extend to a general situation the method for the numerical computation of eigenvalues and eigenvectors of a quasi-diagonal matrix, which is based on a perturbed fixed slope Newton iteration, and whose convergence was proved by the authors in a previous paper, under the hypothesis that the diagonal entries of the matrix are well separated. A generalization to the case of a cluster of diagonal entries is addressed now. Numerical experiments are performed both in the case of an academic example, and in the applied one of a polymer model.