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Solution of an eigenvalue problem for pencils of band matrices

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An iterative algorithm is proposed for solving the complete eigenvalue problem of a regular, linear pencil A-λB of matrices A and B of band structure which under certain conditions preserves the band structure of matrices of the pencil. It is modification of the algorithm AB-1 based on applying nonorthogonal transformations. A detailed description of the algorithm is presented in application to the pencils with tridiagonal and pentadiagonal matrices.

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Literature cited

  1. 1.

    V. N. Kublanovskaya, “On an algorithm for solution of spectral problems of linear matrix pencils,” LOMI Preprint E-1-82, Leningrad (1982).

  2. 2.

    V. N. Kublanovskaya and T. V. Vashchenko, “On a version of the AB algorithm for solving the eigenvalue problem of a regular, linear pencil of matrices,” in: Prikl. Mat. i SAPR v Sudostroenii. Sb. Nuachnykh Trudov, Izd. LKM, Leningrad (1982), pp. 49–60.

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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 139, pp. 41–50, 1984.

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Vashchenko, T.V. Solution of an eigenvalue problem for pencils of band matrices. J Math Sci 36, 199–206 (1987). https://doi.org/10.1007/BF01091800

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  • Band Structure
  • Eigenvalue Problem
  • Iterative Algorithm
  • Band Matrice
  • Linear Pencil