Abstract
Algorithmic methods are presented to perform a priori error analysis and error cumulation comtrol. The corresponding programs are implemented in REDUCE as an extension of Sasaki's multiple precision floating point arithmetic package. Ingredients for the method are some concepts of interval arithmetic and a slightly modified precision notion, in both absolute and relative sense. This allows to take second order effects into account and to consider errors as a combination of inevitable propagated errors, due to inaccurate input, and controlable generated errors, due to arithmetic operations. The error control allows to consider these operations as adjustable sources and results in a set of instructions for using the Sasaki-package such that the precision, dictated by the analysis, guarantees to limit error cumulation to admissible, user chosen error bounds.
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© 1984 Springer-Verlag Berlin Heidelberg
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Hulshof, B.J.A., van Hulzen, J.A. (1984). Automatic error cumulation control. In: Fitch, J. (eds) EUROSAM 84. EUROSAM 1984. Lecture Notes in Computer Science, vol 174. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0032848
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DOI: https://doi.org/10.1007/BFb0032848
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Online ISBN: 978-3-540-38893-7
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