Two-sided Grassmann-Rayleigh quotient iteration
Pierre-Antoine Absil, Paul Van Dooren · 2007
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 ver-sion 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. More-over, Grassmannian versions of the Rayleigh quotient iteration are given for the general-ized Hermitian eigenproblem, the Hamiltonian eigenproblem and the skew-Hamiltonian eigenproblem.