Inverse Iteration: An Alternative Form |
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Authors: | Robert S. Conker Robert J. Lambert |
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Affiliation: | Ames Laboratory—USDOE Iowa State University Ames, Iowa 50010, USA |
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Abstract: | Rayleigh quotient inverse iteration (RQI) is examined from the standpoint of incremental vectors. By choosing such a vector orthogonal to the eigenvector iterate at the mth step, χm, a system of linear equations is derived; solving the system is shown to be equivalent to RQI. The residual norm converges to zero for Hermitian matrices, and the coefficient matrix does not in general converge to a singular matrix as it does in RQI. Furthermore, the procedure described produces successive vector iterates whose norms do not in general become large (when m→∞) as they do with RQI. |
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