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Solution of the eigenvalue problem for the regular bundleD(λ)=λA 0−A 1 using deflated subspaces

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Abstract

We consider the solution of the generalized eigenvalue problem

$$\left( {A_0 \Lambda - A_1 } \right)x = 0,$$

in the case where one or both of the matrices A0, A1 are degenerate but the intersection of their null spaces is empty. Using orthogonal matrices ℘ and which are independent ofλ the original problem is transformed to a simpler one in which the pencil is of smaller dimension. The construction of ℘ and Q uses the normalization process. We include an Algol program and sample runs.

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Authors
  1. T. Ya. Kon'kova
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 88, pp. 48–65, 1978.

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Kon'kova, T.Y. Solution of the eigenvalue problem for the regular bundleD(λ)=λA 0−A 1 using deflated subspaces. J Math Sci 28, 306–318 (1985). https://doi.org/10.1007/BF02104304

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  • DOI: https://doi.org/10.1007/BF02104304

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