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Reliable Computing

, Volume 1, Issue 1, pp 9–14 | Cite as

Formulas for the width of interval products

  • Helmut Ratschek
  • Jon G. Rokne
Mathematical Research

Abstract

Sharp formulas for the width of the product of intervals are derived which are simpler and more effective than the ones previously known. These formulas are useful in applications and they are appropriate tools for estimating the quality of interval evaluations. Proofs of such formulas will, in general, result in a number of different cases involving longwinded calculations. By utilizing certain functionals which are invariants of appropriate interval transformations the calculations are reduced to the ones required for a minimum number of cases.

Keywords

Mathematical Modeling Computational Mathematic Industrial Mathematic Interval Evaluation Interval Product 
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.

Формулы для вычисления ширины интервальных произведений

Abstract

Прелставлены точные формулы для вычнсления шнрнны произвеления нитервалов, являющиеся как более простыми, так н более зффективными, чем нспользовавшиеся до снх пор. Зти формулы могут быть полезны для приложений; кроме того, они прелставляют собой хорошнй ииструмент для оценки качества нитервального оиенивания. Доказтезательства таких формпл, вообше говоря, требппт разбора большого числа числа случаеВ и, соотсвенио, обБемных вычислений. Применение функкпионалов, инвариантных по отношений к определеннум интервальным преобразоаниям, позволило сократить сократить до минимума число слудаев иобБем вычислений.

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Copyright information

© H. Ratschek, J. Rokne 1995

Authors and Affiliations

  • Helmut Ratschek
    • 1
  • Jon G. Rokne
    • 2
  1. 1.Mathematisches Institut der Universität DüsseldorfGermany
  2. 2.Dept. of Computer ScienceThe University of CalgaryCanada

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