• DocumentCode
    1744236
  • Title

    A Grassmann-Rayleigh quotient iteration for computing invariant subspaces

  • Author

    Absil, P.-A. ; Mahony, Robert ; Sepulchre, R. ; Van Dooren, P.

  • Author_Institution
    Inst. Montefiore, Liege Univ., Belgium
  • Volume
    5
  • fYear
    2000
  • fDate
    2000
  • Firstpage
    4241
  • Abstract
    The classical Rayleigh quotient iteration (RQI) computes a 1-dimensional invariant subspace of a symmetric matrix A with cubic convergence. We propose a generalization of the RQI which computes a p-dimensional invariant subspace of A. The geometry of the algorithm on the Grassmann manifold Gr(p,n) is developed to show cubic convergence and to draw connections with Newton algorithms on Riemannian manifolds
  • Keywords
    convergence; geometry; iterative methods; matrix algebra; 1-dimensional invariant subspace; Grassmann manifold; Grassmann-Rayleigh quotient iteration; Riemannian manifolds; cubic convergence; p-dimensional invariant subspace; symmetric matrix; Computational geometry; Convergence; Costs; Displays; Eigenvalues and eigenfunctions; Instruments; Mathematics; Matrix decomposition; Q factor; Riccati equations;
  • fLanguage
    English
  • Publisher
    ieee
  • Conference_Titel
    Decision and Control, 2000. Proceedings of the 39th IEEE Conference on
  • Conference_Location
    Sydney, NSW
  • ISSN
    0191-2216
  • Print_ISBN
    0-7803-6638-7
  • Type

    conf

  • DOI
    10.1109/CDC.2001.914565
  • Filename
    914565
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=1744236