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Solution of the partial eigenvalue problem for a regular matrix pencilD(λ) =A − λB

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Abstract

One presents the ALGOL procedures which implement the algorithm for the determination of the group of smallest (greatest) eigenvalues and their corresponding eigenvectors for a matrix pencil

where A and B are real square matrices of simple structure. From the initial pencil one constructs a matrix C, whose eigenvalues are taken as the initial approximations to the eigenvalues from the group of the smallest (greatest) eigenvalues of the pencil. The refinement of the eigen-values is performed on the basis of the theory of perturbations. Then one determines the eigen-vectors and one computes the infinite norm of the residual. One gives ALGOL programs and test examples.

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Literature cited

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Authors
  1. L. T. Savinova
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 102, pp. 111–122, 1980.

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Savinova, L.T. Solution of the partial eigenvalue problem for a regular matrix pencilD(λ) =A − λB . J Math Sci 22, 1231–1239 (1983). https://doi.org/10.1007/BF01460275

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  • DOI: https://doi.org/10.1007/BF01460275

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