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Computation of eigenvalues of perturbed discrete semibounded operators

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Abstract

To compute the eigenvalues of a perturbed discrete semibounded operator, systems are obtained for the first time in which the number of equations is equal to the multiplicity of the corresponding eigenvalues of the unperturbed operator.

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References

  1. V. A. Sadovnichii and V. V. Dubrovskii, “Remark on a New Method of Calculation of Eigenvalues and Eigenfunctions for Discrete Operators,” Tr. Semin. im. I.G. Petrovskogo, No. 17, 244–248 (1994).

  2. V. A. Sadovnichii and V. E. Podol’skii, “On Computing First Eigenvalues of the Sturm-Liouville Operator,” Dokl. Akad. Nauk 346, 162–164 (1996) [Dokl. Math. 53, 25–27 (1996)].

    MATH  MathSciNet  Google Scholar 

  3. A. A. Dorodnitsyn, “Asymptotic Laws of Eigenvalue Distributions for Some Types of Second-Order Differential Equations,” Usp. Mat. Nauk 7(6), 3–96 (1952).

    Google Scholar 

  4. L. A. Dikii, “New Method of Computing Approximate Eigenvalues of the Sturm-Liouville Problem,” Dokl. Akad. Nauk SSSR 116, 12–14 (1957).

    MATH  MathSciNet  Google Scholar 

  5. L. A. Dikii, “Formulas for Sturm-Liouville Differential Operators,” Usp. Mat. Nauk 13(3), 111–143 (1958).

    MATH  MathSciNet  Google Scholar 

  6. S. A. Shkarin, “On the Gelfand-Dikii Calculation Method for the First Eigenvalues of the Sturm-Liouville Operator,” Vestn. Mosk. Univ., Ser. 1: Mat. Mekh., No. 1, 39–44 (1996).

  7. S. I. Kadchenko, Doctoral Dissertation in Mathematics and Physics (MaGU, Magnitogorsk, 2004).

    Google Scholar 

  8. V. A. Sadovnichii, V. V. Dubrovskii, S. I. Kadchenko, and V. F. Kravchenko, “Evaluation of the First Eigenvalues of the Boundary-Value Hydrodynamic Stability Problem for a Flow between Two Parallel Planes at Small Reynolds Numbers,” Dokl. Akad. Nauk 355, 600–604 (1997) [Dokl. Math. 56, 581–585 (1997)].

    MATH  MathSciNet  Google Scholar 

  9. V. V. Dubrovskii, S. I. Kadchenko, V. F. Kravchenko, and V. A. Sadovnichii, “A New Method for Approximate Evaluation of the First Eigenvalues in the Orr-Sommerfeld Eigenvalue Problem,” Dokl. Akad. Nauk 378, 443–446 (2001) [Dokl. Math. 63, 355–358 (2001)].

    MATH  MathSciNet  Google Scholar 

  10. V. V. Dubrovskii, S. I. Kadchenko, V. F. Kravchenko, and V. A. Sadovnichii, “A New Method for Approximate Evaluation of the First Eigenvalues in the Spectral Problem of Hydrodynamic Stability of Poiseuille Flow in a Circular Pipe,” Dokl. Akad. Nauk 380, 160–163 (2001) [Dokl. Math. 64, 165–168 (2001)].

    MATH  MathSciNet  Google Scholar 

  11. V. A. Sadovnichii, Theory of Operators (Kluwer Academic, New York, 1991; Vysshaya Shkola, Moscow, 1999).

    Google Scholar 

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Original Russian Text © S.I. Kadchenko, I.I. Kinzina, 2006, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2006, Vol. 46, No. 7, pp. 1265–1272.

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Kadchenko, S.I., Kinzina, I.I. Computation of eigenvalues of perturbed discrete semibounded operators. Comput. Math. and Math. Phys. 46, 1200–1206 (2006). https://doi.org/10.1134/S0965542506070116

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  • DOI: https://doi.org/10.1134/S0965542506070116

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