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    • An improved numerical approximation for the first derivative

      Robert De Levie

      Volume 121 Issue 5 September 2009 pp 935-950

    • Fulltext

       

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/jcsc/121/05/0935-0950

    • Keywords

       

      Numerical differentiation; algorithms.

    • Abstract

       

      The traditional numerical computation of the first derivative $f'(x)$ of a given function $f(x)$ of a single argument 𝑥 by central differencing is known to involve aspects of both accuracy and precision. By analysing both we arrive at an algorithm that closely approximates the most accurate answer obtainable by this method, typically with at least 9 accurate decimals, while preserving a minimal footprint. The results apply to software based on the IEEE-754 specification, and are illustrated with Excel.

    • Author Affiliations

       

      Robert De Levie1

      1. Chemistry Department, Bowdoin College, Brunswick ME 04011, USA

    • Dates

       
      Published
      September 2009

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