Skip to main content
Log in

Machine error of parallel algorithms

  • Published:
Cybernetics Aims and scope

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. V. V. Voevodin, Numerical foundations of Linear Algebra [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  2. I. N. Molchanov, On certain difficulties in the solving of applied problems on computers. Preprint No. 79–5, Inst. of Cybernetics, Academy of Sciences of the Ukrainian SSR, Kiev (1979).

    Google Scholar 

  3. J. H. Wilkinson, The Algebraic Eigenvalue Problem, Claredon Press, Oxford (1965).

    Google Scholar 

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

    Google Scholar 

  5. G. E. Eorsythe, M. A. Malcom, and C. B. Moler, Computer Methods for Mathematical Computations, Prentice-Hall, Englewood Cliffs (1977).

    Google Scholar 

  6. V. V. Voevodin, Certain computer aspects of the parallellization of computations. Mathematical Seminar, “Problems of Numerical Mathematics,” Preprint No. 22, VINITI, Moscow (1981).

    Google Scholar 

  7. I. Mikloshko, “Relation between algorithms, programs, and the structure of parallel computers,” in: Algorithms, Software, and the Architecture of Computational Systems, [in Russian], Nauka, Moscow (1982), pp. 6–36.

    Google Scholar 

  8. D. J. Evans (ed.), Parallel Processing Systems, Cambridge University Press, Cambrridge (1982).

    Google Scholar 

  9. I. V. Prangishvili, Microprocessors and Local Nets of Microcomputers in Distributed Control Systems [in Russian], Energoatomizdat, Moscow (1985).

    Google Scholar 

  10. I. Mikloshko, “The complexity of parallel algorithms,” in: Algorithms, software, and the Architecture of Microprocessor Computational Systems [in Russian], Nauka, Moscow (1982), pp. 241–253.

    Google Scholar 

  11. V. I. Solodovnikov, “Upper bounds of complexity of the solution of systems of linear equations,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,118, 159–187 (1982).

    Google Scholar 

  12. G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers, McGraw-Hill, New York (1961).

    Google Scholar 

  13. V. N. Faddeeva and D. K. Faddeev, “Parallel calculations in linear algebra,” Kibernetika, No. 6, 28–40 (1977).

    Google Scholar 

  14. V. N. Faddeeva and D. K. Faddeev, “Parallel calculations in linear algebra. II,” Kibernetika, No. 3, 18–31 (1982).

    Google Scholar 

  15. Ya. E. Romm, Parallel stable variant of the Leverrier-Faddeev method. TRTI (1985). Manuscript deposited with VINITI, No. 5005-85, July 12, 1985.

  16. Ya. E. Romm, “On the acceleration of linear stationary iterative processes in multiprocessor computers. I,” Kibernetika., No. 1, 47–54 (1982).

    Google Scholar 

  17. Ya. E. Romm, “On the acceleration of linear stationary iterative processes in multiprocessor computers. II,” Kibernetika. No. 3, 64–67 (1982).

    Google Scholar 

  18. D. K. Faddeev and V. N. Faddeeva, Computational Methods of Linear Algebra, Freeman, San Francisco (1963).

    Google Scholar 

  19. A. N. Kolmogorov and S. Fomin, Elements of the Theory of Functions and Functional Analysis [in Russian], Nauka, Moscow (1976).

    Google Scholar 

  20. “Development of a vector matrix processor with a high degree of parallelism of operations in the basis of the microprocessors,” Report on Scientific Research, Institute of Cybernetics of the Academy of Sciences of the Ukrainian SSR, directed by Z. L. Rabinovich, GR 79048224; Inv. No. 02821033980, Kiev (1982).

  21. N. S. Bakhvalov, Numerical Methods, Vol. I [in Russian], Nauka, Moscow (1975).

    Google Scholar 

  22. I. S. Berezin and N. G. Zhidkov, Computing Methods, Vol. I [in Russian], Nauka, Moscow (1970).

    Google Scholar 

  23. I. S. Berezin and N. G. Zhidkov, Computing Methods, Vol. II, [in Russian], Nauka, Moscow (1962).

    Google Scholar 

  24. O. N. P'yavchenko and Ya. E. Romm, “A modification of the tabular-interpolation method for the computation of elementary functions on a computer” in: Design Problems and the Application of Discrete Systems in Control. Abstracts of Communications, I, Internat. Conference of Young Scientists, Minsk (1977)-VINITI, Lyubertsy (1977), pp. 326–328.

    Google Scholar 

Download references

Authors

Additional information

Translated from Kibernetika, No. 2, pp. 19–26, March–April, 1988.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Surzhenko, I.F., Romm, Y.E. Machine error of parallel algorithms. Cybern Syst Anal 24, 160–170 (1988). https://doi.org/10.1007/BF01082604

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01082604

Keywords

Navigation