Paper ID sheet UCL-INMA-2005.135


A truncated-CG style method for symmetric generalized eigenvalue problems

P.-A. Absil, C. G. Baker, K. A. Gallivan
A numerical algorithm is proposed for computing an extreme eigenpair of a symmetric/positive-definite matrix pencil $(A,B)$. The leftmost or the rightmost eigenvalue can be targeted. Knowledge of $(A,B)$ is only required through a routine that performs matrix-vector products. The method has excellent global convergence properties and its local rate of convergence is superlinear. It is based on a constrained truncated-CG trust-region strategy to optimize the Rayleigh quotient, in the framework of a recently-proposed trust-region scheme on Riemannian manifolds.
Key words
Journal of Computational and Applied Mathematics, Volume 189, Issues 1-2, 1 May 2006, Pages 274-285
BibTeX entry

  author = "Absil, P.-A. and Baker, C. G. and Gallivan, K. A.",
  title= "A truncated-{CG} style method for symmetric generalized eigenvalue problems",
  journal = "J. Comput. Appl. Math.",
  fjournal = "Journal of Computational and Applied Mathematics",
  volume = 189,
  number = "1--2",
  year = 2006,
  pages = "274--285",
  date_full = "1 May 2006",
Further information