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Solution of the eigenvalue problem for a regular pencil λA0−A1 with singular matrices

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Abstract

One considers the generalized eigenvalue problem (A0λ−A1)x=0, (1) when one or both matrices A0,A1 are singular and ker A0 ∩ ker A1=φ is the empty set. With the aid of the normalized process, the solving of problem (1) reduces to the solving of the eigenvalue problem of a constant matrix of order r=min (r0,r1), where r0,r1 are the ranks of the matrices A0,A1, which are determined at the normalized decomposition of the matrices. One gives an Algol program which performs the presented algorithm and testing examples.

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Literature cited

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Authors
  1. V. N. Kublanovskaya
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  2. T. Ya. Kon'kova
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 70, pp. 103–123, 1977.

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Kublanovskaya, V.N., Kon'kova, T.Y. Solution of the eigenvalue problem for a regular pencil λA0−A1 with singular matrices. J Math Sci 23, 1950–1965 (1983). https://doi.org/10.1007/BF01093277

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  • DOI: https://doi.org/10.1007/BF01093277

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