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Molchanov, I. N.

Machine mathematics: problems and prospects. (English. Russian original) Zbl 1079.68645

Cybern. Syst. Anal. 40, No. 6, 842-848 (2004); translation from Kibern. Sist. Anal. 2004, No. 6, 65-72 (2004).
Summary: “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.

Cited in 1 Document

MSC:

68U99 Computing methodologies and applications
00A35 Methodology of mathematics
00A79 Physics

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

Software:

LINPACK
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Full Text: DOI

References:

[1] http://www.nafems.
[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).
[3] I. N. Molchanov, Machine Methods of Solution of Applied Problems: Algebra and Approximation of Functions [in Russian], Naukova Dumka, Kiev (1987). · Zbl 0685.65011
[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).
[5] J. J. Dongarra, C. B. Moler, J. R. Bunch, and G. W. Steward, LINPACK User’s Guide, SIAM, Philadelphia (1979).
[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).
[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). · Zbl 1029.68164
[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).
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