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Formally Verified Approximations of Definite Integrals

  • Assia Mahboubi
  • Guillaume Melquiond
  • Thomas Sibut-Pinote
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9807)

Abstract

Finding an elementary form for an antiderivative is often a difficult task, so numerical integration has become a common tool when it comes to making sense of a definite integral. Some of the numerical integration methods can even be made rigorous: not only do they compute an approximation of the integral value but they also bound its inaccuracy. Yet numerical integration is still missing from the toolbox when performing formal proofs in analysis.

This paper presents an efficient method for automatically computing and proving bounds on some definite integrals inside the Coq formal system. Our approach is not based on traditional quadrature methods such as Newton-Cotes formulas. Instead, it relies on computing and evaluating antiderivatives of rigorous polynomial approximations, combined with an adaptive domain splitting. This work has been integrated to the CoqInterval library.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Assia Mahboubi
    • 1
  • Guillaume Melquiond
    • 1
    • 2
  • Thomas Sibut-Pinote
    • 1
  1. 1.InriaPalaiseauFrance
  2. 2.LRI, CNRS UMR 8623Université Paris-SudOrsayFrance

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