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.

• Paper: PS file.