TY - RPRT
T1 - Accelerating the LSTRS Algorithm
AU - Lampe, J.
AU - Rojas Larrazabal, Marielba de la Caridad
AU - Sorensen, D.C.
AU - Voss, H.
PY - 2009
Y1 - 2009
N2 - 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.
AB - 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.
M3 - Report
T3 - IMM-Technical Report-2009-09
BT - Accelerating the LSTRS Algorithm
PB - Technical University of Denmark, DTU Informatics, Building 321
CY - Kgs. Lyngby
ER -