Skip to main content
Log in

Minimization of the computational labor in determining the first eigenvalues of differential operators

  • Published:
Mathematical notes of the Academy of Sciences of the USSR Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Literature cited

  1. E. G. D'yakonov and M. Yu. Orekhov, “On minimization of the computational labor in eigenvalue problems,” Dokl. Akad. Nauk SSSR,235, No. 5, 1005–1008 (1977).

    Google Scholar 

  2. E. G. D'yakonov, “Some classes of spectrally equivalent operators, and applications of them,” in: Variational-Difference Methods in Mathematical Physics [in Russian], Sib. Otd. Akad. Nauk SSSR, Novosibirsk (1976), pp. 49–62.

    Google Scholar 

  3. E. G. D'yakonov, “On certain modifications of projection-difference methods,” Vestn. Mosk. Gos. Univ., Ser. Vychisl. Mat. Kibernetiki,1, No. 2, 3–19 (1977).

    Google Scholar 

  4. E. G. D'jakonov, “On triangulations in the finite element method and efficient iterative methods,” Topics in Numer. Anal., Vol. 3, Academic Press, London (1977), pp. 385–404.

    Google Scholar 

  5. E. G. D'yakonov, “On the use of sequences of grids for solving strongly elliptic systems,” in: Computational Methods of Linear Algebra [in Russian], Sib. Otd. Akad. Nauk SSSR, Novosibirsk (1977), pp. 146–162.

    Google Scholar 

  6. E. G. D'yakonov, “Asymptotic minimization of the computational labor in the application of projection-difference methods,” in: Variational-Difference Methods, Sib. Otd. Akad. Nauk SSSR, Novosibirsk (1978), pp. 149–164.

    Google Scholar 

  7. G. P. Astrakhantsev, “Iterational refinement of eigenvalues,” Zh. Vychisl. Mat. Mat. Fiz.,16, No. 1, 131–139 (1976).

    Google Scholar 

  8. G. Strang and G. J. Fix, An Analysis of the Finite Element Method, Prentice-Hall, Englewood Cliffs, New Jersey (1973).

    Google Scholar 

  9. R. S. Varga, Functional Analysis and Approximation Theory in Numerical Analysis, SIAM, Philadelphia (1971).

    Google Scholar 

  10. L. A. Oganesyan, V. Ya. Rivkind, and L. A. Rukhovets, “Variational-difference methods for solving elliptic equations. I,” in: Differential Equations and Their Application [in Russian], No. 5, Inst. Fiz. i Mat., Akad. Nauk Litovsk. SSR, Vilnius (1973).

    Google Scholar 

  11. B. A. Samokish, “The method of steepest descent in the problem of the eigenvalues of semibounded operators,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 5, 105–114 (1958).

    Google Scholar 

  12. S. K. Godunov, V. V. Ogneva, and G. P. Prokopov, “On the convergence of a modified method of steepest descent in computing eigenvalues,” in: Partial Differential Equations (Proc. of a symposium to commemorate the 60th birthday of Academician S. L. Sobolev), Nauka, Moscow (1970), pp. 77–80.

    Google Scholar 

  13. V. G. Prikazchikov, “Rigorous estimates of the rate of convergence of an iteration method for computing eigenvalues,” Zh. Vychisl. Mat. Mat. Fiz.,15, No. 5, 1330–1333 (1975).

    Google Scholar 

  14. E. G. D'yakonov, “On some estimates in iterational methods for finding smallest eigenvalues,” in: Numerical Methods in Mathematical Physics [in Russian], Sib. Otd. Akad. Nauk SSSR, Novosibirsk (1979), pp. 155–157.

    Google Scholar 

  15. P. G. Ciariet, M. H. Schultz, and R. S. Varga, “Numerical methods of high-order accuracy for nonlinear boundary value problems, III. Eigenvalue problems,” Numer. Math.,12, No. 2, 120–133 (1968).

    Google Scholar 

  16. R. E. Bank and D. J. Rose, “Extrapolated fast direct algorithms for elliptic boundary value problems,” Algorithms and Complexity: New Directions and Recent Results (Proc. Sympos. Carnegie-Mellon Univ.), New York (1976), pp. 201–249.

  17. N. S. Bakhvalov, Numerical Methods [in Russian], Nauka, Moscow (1973).

    Google Scholar 

  18. V. G. Korneev, High-Order Schemes for the Finite-Element Method [in Russian], Leningrad State Univ. (1977).

  19. A. M. Matsokin, “A variational-difference method for solving elliptic equations in three-dimensional regions,” in: Variational-Difference Methods in Mathematical Physics [in Russian], Sib. Otd. Akad. Nauk SSSR, Novosibirsk (1976), pp. 124–129.

    Google Scholar 

  20. E. G. D'yakonov, “On come direct and iterational methods based on bordering a matrix,” in: Numerical Methods in Mathematical Physics [in Russian], Sib. Otd. Akad. Nauk SSSR, Novosibirsk (1979), pp. 45–68.

    Google Scholar 

  21. Yu. A. Kuznetsov, “Block-relaxation methods in a subspace for two-dimensional elliptic equations,” in: Numerical Methods in Mathematical Physics [in Russian], Sib. Otd. Akad. Nauk SSSR, Novosibirsk (1979), pp. 20–44.

    Google Scholar 

  22. E. G. D'yakonov, “On some methods for solving the systems of equations of difference and projection-difference schemes,” in: Computational Methods of Linear Algebra [in Russian], Sib. Otd. Akad. Nauk SSSR, Novosibirsk (1972), pp. 28–58.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Matematicheskie Zametki, Vol. 27, No. 5, pp. 795–812, May, 1980.

Rights and permissions

Reprints and permissions

About this article

Cite this article

D'yakonov, E.G., Orekhov, M.Y. Minimization of the computational labor in determining the first eigenvalues of differential operators. Mathematical Notes of the Academy of Sciences of the USSR 27, 382–391 (1980). https://doi.org/10.1007/BF01139851

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01139851

Keywords

Navigation