Estimation of the Derivatives of a Digital Function with a Convergent Bounded Error

  • Laurent Provot
  • Yan Gérard
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6607)

Abstract

We provide a new method to estimate the derivatives of a digital function by linear programming or other geometrical algorithms. Knowing the digitization of a real continuous function f with a resolution h, this approach provides an approximation of the k th derivative f (k)(x) with a maximal error in \(O(h^{\frac{1}{1+k}})\) where the constant depends on an upper bound of the absolute value of the (k + 1) th derivative of f in a neighborhood of x. This convergence rate \(\frac{1}{k+1}\) should be compared to the two other methods already providing such uniform convergence results, namely \(\frac{1}{3}\) from Lachaud et. al (only for the first order derivative) and \((\frac{2}{3})^k\) from Malgouyres et al..

Keywords

Derivative estimation Digital Level Layer Convergence rate Linear Programming 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Laurent Provot
    • 1
  • Yan Gérard
    • 1
  1. 1.ISITUniv. Clermont 1AubièreFrance

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