An Implicit Riemannian Trust-Region Method for the Symmetric Generalized Eigenproblem

  • C. G. Baker
  • P. -A. Absil
  • K. A. Gallivan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3991)


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.


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© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • C. G. Baker
    • 1
    • 2
  • P. -A. Absil
    • 3
    • 4
  • K. A. Gallivan
    • 1
  1. 1.School of Computational ScienceFlorida State UniversityTallahasseeUSA
  2. 2.Computational Mathematics & AlgorithmsSandia National LaboratoriesAlbuquerqueUSA
  3. 3.Département d’ingénierie mathématiqueUniversité catholique de LouvainLouvain-la-NeuveBelgium
  4. 4.PeterhouseUniversity of CambridgeUK

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