Rayleigh quotient algorithms for nonsymmetric matrix pencils |
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Authors: | A Amiraslani P Lancaster |
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Institution: | (1) Department of Mathematics and Statistics, University of Calgary, 2500 University Dr. NW, Calgary, AB, T2N 1N4, Canada |
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Abstract: | A classical Rayleigh-quotient iterative algorithm (known as “broken iteration”) for finding eigenvalues and eigenvectors is
applied to semisimple regular matrix pencils A − λB. It is proved that cubic convergence is attained for eigenvalues and superlinear convergence of order three for eigenvectors.
Also, each eigenvalue has a local basin of attraction. A closely related Newton algorithm is examined. Numerical examples
are included.
Dedicated to the memory of Gene H. Golub. |
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Keywords: | Rayleigh quotient algorithm Matrix pencils |
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