Skip to main content
Log in

Sharp a priori error estimates of the Rayleigh-Ritz method without assumptions of fixed sign or compactness

  • 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. F. Chatelin, Spectral Approximation of Linear Operators, Academic Press, New York (1983).

    Google Scholar 

  2. R. S. Varga, Functional Analysis and Approximation Theory in Numerical Analysis, Society for Industrial and Applied Mathematics, Philadelphia (1971).

    Google Scholar 

  3. G. Strang and G. Fix, An analysis of the Finite Element Method, Pentice-Hall, Englewood Cliffs (1973).

    Google Scholar 

  4. E. G. D'yakonov and M. Yu. Orekhov, “On the minimization of computational work in the determination of the first eigenvalues of differential operators,” Mat. Zametki,27, No. 5, 795–812 (1980).

    Google Scholar 

  5. B. Parlett, The Symmetric Eigenvalue Problem, Prentice-Hall, Englewood Cliffs (1980).

    Google Scholar 

  6. Y. Saad, “Projection methods for solving large sparse eigenvalue problems,” in: B. Kagström and A. Ruhe (eds.), Matrix Pencils, Lecture Notes in Math., Vol. 973, Springer-Verlag, Berlin-New York (1983), pp. 121–144.

    Google Scholar 

  7. E. G. D'yakonov and A. V. Knyazev, “A group iteration method for the determination of the lowest eigenvalues,” Vestn. Mosk. Gos. Univ., Ser.15, Vychisl. Mat. Kibern., No. 2, 29–34 (1982).

    Google Scholar 

  8. A. V. Knyazev, On the Method of Simultaneous Computation of Several Eigenvectors [in Russian], Preprint IAÉ-3724/16, Moscow (1983).

  9. A. V. Knyazev and V. I. Lebedev, “Estimates of the convergence and analysis of optimality of iteration methods of simultaneous computation of several eigenvectors,” in: Computational Methods of Linear Algebra [in Russian], Otd. Vychisl. Mat. Akad. Nauk SSSR, Moscow (1983), pp. 94–114.

    Google Scholar 

  10. M. A. Krasnosel'skii, G. M. Vainikko, P. P. Zabreiko, and others, Approximate Solution of Operator Equations [in Russian], Nauka, Moscow (1969).

    Google Scholar 

  11. A. V. Knyazev, “On sharp a priori error estimates of the type of inequalities in the Rayleigh-Ritz method for symmetric spectral problems without the assumptions of fixed sign or compactness,” in: Methods of Computational and Applied Mathematics [in Russian], Otd. Vychisl. Mat. Akad. Nauk SSSR, Moscow (1985), pp. 74–88.

    Google Scholar 

  12. M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. 4, Analysis of Operators, Academic Press, New York (1978).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Matematicheskie Zametki, Vol. 38, No. 6, pp. 900–907, December, 1985.

The main aim of this note from the beginning has been the generalization of the results of [4], in which D'yakonov took the lead. The author is thankful to him.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Knyazev, A.V. Sharp a priori error estimates of the Rayleigh-Ritz method without assumptions of fixed sign or compactness. Mathematical Notes of the Academy of Sciences of the USSR 38, 998–1002 (1985). https://doi.org/10.1007/BF01157020

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01157020

Keywords

Navigation