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On a certain class of spectral characteristics of matrices

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References

  1. J. H. Wilkinson, The Algebraic Eigenvalue Problem [Russian translation], Nauka, Moscow (1970).

    Google Scholar 

  2. D. K. Faddeev and V. N. Faddeeva, Computational Methods of Linear Algebra [in Russian], Fizmatgiz, Moscow-Leningrad (1963).

    Google Scholar 

  3. A. Ya. Bulgakov, “An effectively calculable parameter of stability quality for systems of linear differential equations with constant coefficients,” Sibirsk. Mat. Zh.,21, No. 3, 32–41 (1980).

    Google Scholar 

  4. S. K. Godunov and A. J. Bulgakov, “Difficultes de calculi dans le probleme de Hurwitz et methodes pour les surmonter,” in: Analysis and Optimization of Systems (Versailles, 1982), Springer, 1982, pp. 843–851.

    Google Scholar 

  5. A. Ya. Bulgakov and S. K. Godunov, “Calculation of positive definite solutions to the Lyapunov equation,” Trudy Inst. Mat. (Novosibirsk). Vol. 6: Numerical Methods of Linear Algebra [in Russian], Nauka, Novosibirsk, 1985, pp. 17–38.

    Google Scholar 

  6. Sh. I. Razzakov, Qualified Estimates for the Convergence Rate of the Voevodin Orthogonal Power Method for Arbitrary Matrices [in Russian], Avtoref. Dis. ... Kand. Fiz.-Mat. Nauk: 01.01.07, Novosibirsk (1984).

  7. S. K. Godunov, “The dichotomy problem for the spectrum of a matrix,” Sibirsk. Mat. Zh.,27, No. 5, 24–37 (1986).

    Google Scholar 

  8. A. Ya. Bulgakov and S. K. Godunov, “Circular dichotomy of the matrix spectrum,” Sibirsk. Mat. Zh.,29, No. 5, 59–70 (1988).

    Google Scholar 

  9. S. K. Godunov, “Criteria for convergence of orthogonal power methods in spectral analysis of matrices,” Trudy Inst. Mat. (Novosibirsk). Vol. 15: Numerical Analysis [in Russian], Nauka, Novosibirsk, 1989, pp. 4–12.

    Google Scholar 

  10. S. K. Godunov, A. G. Antonov, O. P. Kirilyuk, and V. I. Kostin, Guaranteed Accuracy of Solving Linear Equations in Euclidean Spaces [in Russian], Nauka, Novosibirsk (1992).

    Google Scholar 

  11. G. V. Demidenko, To the Question of Determination of Matrices Whose Spectra Lie on the Imaginary Axis [Preprint, No. 12] [in Russian], Inst. Mat. (Novosibirsk), Novosibirsk (1993).

    Google Scholar 

  12. G. V. Demidenko, “Integral operators determined by boundary value problems for quasielliptic equations,” Dokl. RAN,326, No. 5, 765–769 (1992).

    Google Scholar 

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The research was financially supported by the Russian Foundation for Fundamental Research (Grant 93-011-1515).

Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 35, No. 5, pp. 1032–1051, September–October, 1994.

The author is grateful to Professor S. K. Godunov for useful discussions and expresses his gratitude to I. I. Matveeva for carrying out a series of numerical experiments.

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Demidenko, G.V. On a certain class of spectral characteristics of matrices. Sib Math J 35, 917–935 (1994). https://doi.org/10.1007/BF02104569

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