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To the Solution of Partial Eigenproblems for Polynomial Matrices

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Abstract

Methods for computing scalar and vector spectral characteristics of a polynomial matrix are proposed. These methods are based on determining the so-called generating vectors (eigenvectors and principal vectors) by using the method of rank factorization of polynomial matrices. The possibility of extending the methods to the case of two-parameter polynomial matrices is indicated. Bibliography: 4 titles.

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REFERENCES

  1. V. N. Kublanovskaya, “Methods and algorithms for solving spectral problems for polynomial and rational matrices,” Zap. Nauchn. Semin. POMI, 238, 7–329 (1998).

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  2. V. N. Kublanovskaya and V. B. Khazanov, “Deflation in spectral problems for pencils of matrices,” in: Computational Processes and Systems [in Russian], Nauka, Moscow (1987), pp. 138–147.

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  3. V. B. Khazanov, “On spectral properties of λ-matrices,” Zap. Nauchn. Semin. LOMI, 111, 180–194 (1981).

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  4. V. B. Khazanov, “Generating eigenvectors of a multiparameter polynomial matrix,” Zap. Nauchn. Semin. POMI, 248, 165–186 (1998).

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Authors and Affiliations

  1. St.Petersburg Department of the Steklov Mathematical Institute, Russia

    V. N. Kublanovskaya

  2. St.Petersburg Marine Technical University, Russia

    V. B. Khazanov

Authors
  1. V. N. Kublanovskaya
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  2. V. B. Khazanov
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Kublanovskaya, V.N., Khazanov, V.B. To the Solution of Partial Eigenproblems for Polynomial Matrices. Journal of Mathematical Sciences 121, 2530–2537 (2004). https://doi.org/10.1023/B:JOTH.0000026290.16319.a8

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  • DOI: https://doi.org/10.1023/B:JOTH.0000026290.16319.a8

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