Skip to main content
SpringerLink
Log in

To the Theory of the Alternating Triangle Iteration Method

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

Abstract

We construct a new class of versions of the adaptive alternating triangle method whose optimization requires no a priori spectral information in contrast with the approaches known so far. The same estimate for the convergence rate is preserved as in the presence of a priori information.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Samarskii A. A., “On one algorithm of numerical solution of systems of differential and algebraic equations,” Zh. Vychisl. Mat. i Mat. Fiz., 4, No. 3, 580–584 (1964).

    Google Scholar 

  2. Samarskii A. A., The Theory of Difference Schemes [in Russian], Nauka, Moscow (1989).

    Google Scholar 

  3. Samarskii A. A. and Nikolaev E. S., Methods for Solving Grid Equations [in Russian], Nauka, Moscow (1978).

    Google Scholar 

  4. Samarskii A. A. and Gulin A. V., Numerical Methods [in Russian], Nauka, Moscow (1989).

    Google Scholar 

  5. Kantorovich L. V., “On the method of steepest descent,” Dokl. Akad. Nauk SSSR, 56, No. 3, 233–236 (1947).

    Google Scholar 

  6. Kantorovich L. V., “Functional analysis and applied mathematics,” Uspekhi Mat. Nauk, 3, No. 6, 89–185 (1948).

    Google Scholar 

  7. Marchuk G. I. and Kuznetsov Yu. A., Iteration Methods and Quadratic Functionals [in Russian], Nauka, Novosibirsk (1972).

    Google Scholar 

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

    Google Scholar 

  9. Kantorovich L. V. and Akilov G. P., Functional Analysis [Russian], Nauka, Moscow (1977).

    Google Scholar 

  10. Marchuk G. I., Methods of Numerical Mathematics [in Russian], Nauka, Moscow (1980).

    Google Scholar 

  11. Kuznetsov Yu. A., “The method of conjugate gradients, its generalizations and applications,” in: Computing Processes and Systems. Vol. 1 [in Russian], Nauka, Moscow, 1983, pp. 267–301.

    Google Scholar 

  12. Marchuk G. I., Splitting Methods [in Russian], Nauka, Moscow (1988).

    Google Scholar 

  13. Konovalov A. N., “Variational optimization of iterative split methods,” Sibirsk. Mat. Zh., 38, No. 2, 312–325 (1997).

    Google Scholar 

  14. Hardy G. H., Littlewood D. E., and Pólya G., Inequalities [Russian translation], Izdat. Inostr. Lit., Moscow (1948).

  15. Polya G. and Szegoe G., Problems and Theorems in Analysis. Vol. 1 [Russian translation], Izdat. Inostr. Lit., Moscow and Leningrad (1937).

  16. Horn R. and Johnson Ch., Matrix Analysis [Russian translation], Mir, Moscow (1989).

    Google Scholar 

  17. Voevodin V. V. and Kuznetsov Yu. A., Matrices and Calculations [in Russian], Nauka, Moscow (1984).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. The Institute of Computer Mathematics and Mathematical Geophysics, Novosibirsk

    A. N. Konovalov

Authors
  1. A. N. Konovalov
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Konovalov, A.N. To the Theory of the Alternating Triangle Iteration Method. Siberian Mathematical Journal 43, 439–457 (2002). https://doi.org/10.1023/A:1015455317080

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1015455317080

Search

Navigation