Numerical methods for finding multiple eigenvalues of matrices depending on parameters |
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Authors: | Hua Dai Peter Lancaster |
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Institution: | (1) Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P.R. China, CN;(2) Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta T2N 1N4, Canada, CA |
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Abstract: | Summary. Let be a square matrix dependent on parameters and , of which we choose as the eigenvalue parameter. Many computational problems are equivalent to finding a point such that has a multiple eigenvalue at . An incomplete decomposition of a matrix dependent on several parameters is proposed. Based on the developed theory two new algorithms are
presented for computing multiple eigenvalues of with geometric multiplicity . A third algorithm is designed for the computation of multiple eigenvalues with geometric multiplicity but which also appears to have local quadratic convergence to semi-simple eigenvalues. Convergence analyses of these methods
are given. Several numerical examples are presented which illustrate the behaviour and applications of our methods.
Received December 19, 1994 / Revised version received January 18, 1996 |
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Keywords: | Mathematics Subject Classification (1991):65F15 65F30 |
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