Cybernetics and Systems Analysis

, Volume 40, Issue 6, pp 842–848 | Cite as

Machine mathematics: Problems and prospects

  • I. N. Molchanov
Article

Abstract

“Pitfalls” are considered that arise during the implementation of theoretically justified algorithms of computational mathematics in solving scientific and technical problems and lead to computer solutions that have no physical meaning.

Keywords

computer model of a problem error of software implementation of an algorithm reliability of a computer solution computer-oriented algorithm of mathematical investigation computer solution machine mathematics intellectual software 

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REFERENCES

  1. 1.
    http://www.nafems.Google Scholar
  2. 2.
    H. Heuer, I. N. Moltschanow, and F. Stuchlik, “Schwierigkeiten im Zusammenhang mit der Lösung mathematischer Aufgaben auf Computern,” Prepr. No. 2, Otto von Guericke Univ., Magdeburg (1995).Google Scholar
  3. 3.
    I. N. Molchanov, Machine Methods of Solution of Applied Problems: Algebra and Approximation of Functions [in Russian], Naukova Dumka, Kiev (1987).Google Scholar
  4. 4.
    H. Heuer, I. N. Moltschanow, and F. Stuchlik, “Die mathematische Modellierung — Mö glichkeiten und Grenzen,” Prepr. No. 10, Otto von Guericke Univ., Magdeburg (1994).Google Scholar
  5. 5.
    J. J. Dongarra, C. B. Moler, J. R. Bunch, and G. W. Steward, LINPACK User’s Guide, SIAM, Philadelphia (1979).Google Scholar
  6. 6.
    I. M. Molchanov, Ye. F. Galba, O. V. Popov, O. M. Khimich, T. V. Chistyakova, and M. F. Yakovlev, “An intelligent interface for investigation and solution of problems of computational mathematics with approximately specified input data on a MIMD-computer,” Probl. Programmirovaniya, Nos. 1–2, 102–112 (2000).Google Scholar
  7. 7.
    I. N. Molchanov and M. F. Yakovlev, “Algorithmic foundations of creation of an intelligent software tool for investigation and solution of Cauchy problems for systems of ordinary differential equations,” Cybernetics and Systems Analysis, No. 5, 3–16 (2001).Google Scholar
  8. 8.
    I. N. Molchanov, Ye. F. Galba, A. V. Popov, A. N. Khimich, T. V. Chistyakova, and M. F. Yakovlev, “An intelligent interface for investigation and solution of problems of strength analysis of constructions,” Probl. Programmirovaniya, Nos. 1–2, 532–537 (2002).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2004

Authors and Affiliations

  • I. N. Molchanov
    • 1
  1. 1.Cybernetics InstituteNational Academy of Sciences of UkraineKievUkraine

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