Accelerating the LSTRS algorithm

The LSTRS software for the efficient solution of the Large-Scale Trust-Region Subproblem was proposed in [Rojas, Santos, Sorensen: ACM ToMS 34 (2008), Article 11]. The LSTRS method is based on recasting the problem 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 a bordered Hessian matrix (or two smallest eigenvalues in the potential hard case) and associated eigenvector(s). Using the Nonlinear Arnoldi method to solve the eigenvalue problems makes it possible to recycle most of the information from previous iterations which can substantially accelerate LSTRS.Electrical Engineering, Mathematics and Computer Scienc