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Modular analysis of numerical software

Part of the Lecture Notes in Mathematics book series (LNM,volume 773)

Abstract

We have attempted to demonstrate how the design of control modules in numerical software may be based on rigorous analysis to a larger extent. The relative merits of different designs may more reliably be evaluated by simulation experiments than by traditional testing of complete codes. Similarly the values of design parameters within the individual modules may be selected on the basis of such simulations. The detailed presentation of the mathematical models which have guided the design of the various control modules and the description of the simulation (or other) experiments which have established the functioning of the design should be explicitly included in publications about numerical software products. Scientific reporting in other fields of engineering could serve as an example.

It is essential for the further development of Numerical Mathematics that its engineering aspects which are represented by the design, evaluation, and maintenance of numerical software, are fully developed to a level of achievement which is comparable to that of its more theoretical aspects. The establishment of a tradition in reporting about the design of numerical software will give more recognition to the excellent scientific work which is often done in this area, and to those who do it. Also the existence of a collection of well-confirmed or even proven results concerning the design of control modules in numerical software will permit referencing to a much larger extent than it is possible now. It is hoped that the combined efforts of the research scientists working in this area and of the editors and referees of the relevant journals will succeed in establishing such a tradition.

Keywords

  • Control Module
  • Local Error
  • Design Objective
  • Emergency State
  • Numerical Mathematic

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. W.H. Enright: using a testing package for the automatic assessment of numerical methods for ODE’s, in: Performance Evaluation of Numerical Software, Conference Proceedings, North Holland, 1979.

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  2. H.J. Stetter: Interpolation and error estimation in Adams PC-codes, SINUM 16 (1979) 311–323.

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  3. L.F. Shampine, M.K. Gordon: Computer solution of ordinary differential equations, the initial value problem, W.H. Freeman, San Francisco, 1975.

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© 1980 Springer-Verlag

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Stetter, H.J. (1980). Modular analysis of numerical software. In: Watson, G.A. (eds) Numerical Analysis. Lecture Notes in Mathematics, vol 773. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0094169

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  • DOI: https://doi.org/10.1007/BFb0094169

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09740-2

  • Online ISBN: 978-3-540-38562-2

  • eBook Packages: Springer Book Archive