In a recent paper [Rojas, Santos, Sorensen: ACM ToMS 34 (2008), Article 11] an
efficient method for solving the Large-Scale Trust-Region Subproblem was suggested which is based
on recasting it in terms of a parameter dependent eigenvalue problem and adjusting the parameter
iteratively. The essential work at each iteration is the solution of an eigenvalue problem for the
smallest eigenvalue of the Hessian matrix (or two smallest eigenvalues in the potential hard case) and
associated eigenvector(s). Replacing the implicitly restarted Lanczos method in the original paper
with the Nonlinear Arnoldi method makes it possible to recycle most of the work from previous
iterations which can substantially accelerate LSTRS.