# Two-sided Grassmann Rayleigh quotient iteration

- AUTHORS: P.-A. Absil, P. 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 symmetric eigenproblem, the
Hamiltonian eigenproblem and the skew-Hamiltonian eigenproblem.
- STATUS:
In revision.
- DATE OF ENTRY: October 2002.

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