Skip to main content
Log in

The Total Error in Calculating Linear Mathematical Models by Iterative Methods

  • Published:
Cybernetics and Systems Analysis Aims and scope

Abstract

Estimates are derived for the total error in solving linear algebraic systems, including non-consistent ones, by one- and two-step iterative methods, with input data being approximate. Criteria for terminating iterative processes are constructed providing a given accuracy of the solution.

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.

Similar content being viewed by others

REFERENCES

  1. D. K. Faddeev and V. N. Faddeeva, Computing Methods of Linear Algebra [in Russian], Fizmatgiz, Moscow (1960).

    Google Scholar 

  2. M. A. Krasnosel'skii, G. V. Vainikko, P. P. Zabreiko, Ya. B. Rutnitskii, and V. A. Stetsenko, Approximate Solution of Operator Equations [in Russian], Nauka, Moscow (1969).

    Google Scholar 

  3. A. A. Samarskii, Introduction to the Theory of Difference Schemes [in Russian], Nauka, Moscow (1971).

    Google Scholar 

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

    Google Scholar 

  5. G. I. Marchuk, Methods of Computational Mathematics [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  6. A. A. Samarskii and E. S. Nikolaev, Methods of Solution of Mesh Equations [in Russian], Nauka, Moscow (1978).

    Google Scholar 

  7. K. Flatcher, Numerical Methods Based on Galerkin Method [Russian translation], Mir, Moscow (1988).

    Google Scholar 

  8. V. I. Lebedev and S. A. Finogenov, “The order of selecting iterative parameters in the Chebyshev cyclic iterative method,” Zh. Vych. Mat. Mat. Fiz., 11, No. 2, 425-438 (1971).

    Google Scholar 

  9. V. M. Glushkov, I. N. Molchanov, B. N. Brusnikin et al., Software of Mir-1 and Mir-2 Computers. Numerical Methods [in Russian], Vol. 1, Naukova Dumka, Kiev (1976).

    Google Scholar 

  10. E. F. Galba, “Iterative methods for calculation of the weighted normal pseudo-solution with degenerate weights,” Zh. Vych. Mat. Mat. Fiz., 39, No. 6, 886-289 (1999).

    Google Scholar 

  11. E. F. Galba, “Iterative methods to compute weighted normal pseudosolutions with positive definite weights,” Kibern. Sist. Analiz, No. 2, 105-115 (1998).

  12. A. N. Khimich and M. F. Yakovlev, “Solution of SLAE with semi-definite symmetric positive matrices,” in: Computer Mathematics. Optimization of Calculations [in Russian], Vol. 1, V. M. Glushkov Institute of Cybernetics, Sci. Council on Cybernetics (2001), pp. 392-396.

    Google Scholar 

  13. I. N. Molchanov and M. F. Yakovlev, “Iterative processes of solution of a class of incompatible systems of linear algebraic equations,” Zh. Vych. Mat. Mat. Fiz., 15, No. 3, 547-558 (1975).

    Google Scholar 

  14. Ch. Lawson and P. Henson, Numerical Solution of Problems of the Least-Squares Method [Russian translation], Nauka, Moscow (1986).

    Google Scholar 

  15. A. N. Khimich, “Perturbation bounds for the least-squares problem,” Kibern. Sist. Analiz, No. 3, 142-145 (1996).

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Khimich, A.N., Yakovlev, M.F. The Total Error in Calculating Linear Mathematical Models by Iterative Methods. Cybernetics and Systems Analysis 38, 749–758 (2002). https://doi.org/10.1023/A:1021895010938

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1021895010938

Navigation