Paper ID sheet UCL-INMA-2007.024


Two-sided Grassmann-Rayleigh quotient iteration

P.-A. Absil, Paul Van Dooren
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
Numerische Mathematik, Volume 114, Number 4, pp. 549-571, February, 2010
BibTeX entry

  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",