Paper ID sheet UCL-INMA-2007.024

Title

Two-sided Grassmann-Rayleigh quotient iteration

Authors

P.-A. Absil, Paul Van Dooren

Abstract

The two-sided Rayleigh quotient iteration proposed by Ostrowski computes a pair of corresponding left-right eigenvectors of a matrix $C$. We propose a Grassmannian version of this iteration, i.e., its iterates are pairs of $p$-dimensional subspaces instead of one-dimensional subspaces in the classical case. The new iteration generically converges locally cubically to the pairs of left-right $p$-dimensional invariant subspaces of $C$. Moreover, Grassmannian versions of the Rayleigh quotient iteration are given for the generalized Hermitian eigenproblem, the Hamiltonian eigenproblem and the skew-Hamiltonian eigenproblem.

Key words

Block Rayleigh quotient iteration; two-sided iteration; Grassmann manifold; generalized eigenproblem; Hamiltonian eigenproblem

Status

Numerische Mathematik, Volume 114, Number 4, pp. 549-571, February, 2010

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• Publisher's version: doi:10.1007/s00211-009-0266-y
• Preprint

BibTeX entry

  @ARTICLE{AbsDoo2010,
  author = "P.-A. Absil and P. Van Dooren",
  title = "Two-sided Grassmann-Rayleigh quotient iteration",
  journal = "Numer. Math.",
  fjournal = "Numerische Mathematik",
  year = 2010,
  month = "February",
  volume = 114,
  number = 4,
  pages = "549-571",
}