• TITLE: An Implicit Riemannian Trust-Region Method for the Symmetric Generalized Eigenvalue Problem
• AUTHORS: C. G. Baker, P.-A. Absil, K. A. Gallivan.
• ABSTRACT:
  The recently proposed Riemannian Trust-Region method can be applied to the problem of computing extreme eigenpairs of a matrix pencil, with strong global convergence and local convergence properties. This paper addresses inherent inefficiencies of an explicit trust-region mechanism. We propose a new algorithm, the Implicit Riemannian Trust Region method for extreme eigenpair computation, which seeks to overcome these inefficiencies while still retaining the favorable convergence properties.
• STATUS: published in Lecture Notes in Computer Science, Volume 3991 / 2006. Proceedings of the 6th International Conference on Computational Science, Reading, U.K., May 28-31, 2006.
• DATE OF ENTRY: February 2006.

• Published version: doi:10.1007/11758501_32.
• Preprint [pdf]
• ICCS06 conference presentation [pdf]
• Extended version. Technical Report FSU-SCS-2006-152, February 2006, accessible from SCS ePrints
• Related papers:
  1. An Implicit Trust-Region Methods on Riemannian Manifolds
  2. Trust-region methods on Riemannian manifolds
  3. A truncated-CG style method for symmetric generalized eigenvalue problems
  4. Adaptive model trust region methods for generalized eigenvalue problems
• Other set of slides: [pdf]

BibTeX citation:

@inproceedings{LNCS39910210,
   editor    = {Vassil N. Alexandrov and Geert Dick van Albada and Peter M.A. Sloot and Jack Dongarra},
   booktitle = {Computational Science -- ICCS 2006},
   publisher = {Springer},
   series    = {LNCS},
   volume    = {3991},
   year      = {2006},
   isbn      = {3-540-34379-2},
   author    = {C. G. Baker and P.-A. Absil and K. A. Gallivan},
   title     = {An Implicit {Riemannian} Trust-Region Method for the Symmetric Generalized Eigenproblem},
   pages     = {210--217}
}