The error in interval arithmetic

  • Webb Miller
Part of the Lecture Notes in Computer Science book series (LNCS, volume 29)


It is widely appreciated that interval arithmetic can yield overly pessimistic results because it ignores correlations among intermediate values. One approach toward understanding this phenomenon begins by disregarding "second-order effects" and rounding errors. An early result of this type is Hansen's proof of Moore's conjecture that the centered form "converges quadratically", i.e., produces exact results under the simplifying assumptions.

Here we give a simple derivation of expressions for the first-order effects of error in interval arithmetic. These results can serve as the basis for proofs of a number of known results.


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    Goldstein, A. and Richman, P., A midpoint phenomenon. JACM 20 (1973), 301–304.CrossRefGoogle Scholar
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    Hansen, E., The centered form, in Topics in Interval Analysis, E. Hansen, ed., Clarendon, Oxford, 1969.Google Scholar
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    Miller, W., Quadratic convergence in interval arithmetic, part II, BIT 12 (1972), 291–298.Google Scholar
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    Miller, W., More on quadratic convergence in interval arithmetic. BIT 13 (1973), 76–83.Google Scholar
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Copyright information

© Springer-Verlag Berlin Heidelberg 1975

Authors and Affiliations

  • Webb Miller
    • 1
  1. 1.Computer Science DepartmentThe Pennsylvania State UniversityUniversity Park

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