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Spectral problem for polynomial matrix pencils. 2

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Abstract

For an arbitrary polynomial pencil

of matrices Ai of dimensions m×n one presents an algorithm for the computation of the eigenvalues of the regular kernel of the pencil. The algorithm allows to construct a regular pencil having the same eigenvalues as the regular kernel of the initial pencil or (in the case of a dead end termination) allows to pass from the initial pencil to a pencil of smaller dimensions whose regular kernel has the same eigenvalues as the initial pencil. The problem is solved by reducing the obtained pencil to a linear one. For solving the problem in the case of a linear pencil one considers algorithms for pencils of full column rank as well as for completely singular pencils.

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Literature cited

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Authors
  1. V. N. Kublanovskaya
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 111, pp. 109–116, 1981.

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Kublanovskaya, V.N. Spectral problem for polynomial matrix pencils. 2. J Math Sci 24, 69–75 (1984). https://doi.org/10.1007/BF01230267

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  • DOI: https://doi.org/10.1007/BF01230267

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