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.


Riemannian Manifold Outer Iteration Sandia National Laboratory Generalize Eigenvalue Problem Grassmann Manifold 
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Copyright information

© 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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