Two-sided Grassmann-Rayleigh quotient iteration

Details Two-sided Grassmann-Rayleigh quotient iteration Two-sided Grassmann-Rayleigh quotient iteration

2008-03-28

arxiv.org/abs/0803.4179v1

Numer.Math.114:549-571,2010

Mathematics

Numerical Analysis

The text is identical to a manuscript that was submitted for publication on 19 April 2007

Scientific paper

10.1007/s00211-009-0266-y

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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