Two-sided Grassmann-Rayleigh quotient iteration

Absil, Pierre-Antoine;Van Dooren, Paul
(2010) Numerische Mathematik — Vol. 114, p. 549-571 (2010)

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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.
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Absil, P.-A., & Van Dooren, P. (2010). Two-sided Grassmann-Rayleigh quotient iteration. Numerische Mathematik, 114, 549-571. https://doi.org/10.1007/s00211-009-0266-y (Original work published 2010)