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Intégration numérique avec erreur bornée en précision arbitraire

Abstract : Numerical integration is commonly available in numerical computation systems. We study in this thesis the error on the result of a numerical quadrature using the Newton-Cotes and Gauss-Legendre methods for a monodimensional real function in the context of arbitrary precision. From the algorithmic point of view we give for each method a computation procedure with a guaranteed bound on the error. For the analysis of the Gauss-Legendre method we studied polynomial root refinement schemes (secante, Newton's iteration, dichotomy) and we gave heuristics to make sure the method converges in practice. The algorithms proposed in this thesis were written in a numerical quadrature library called "Correctly Rounded Quadrature" (CRQ) available at We also give a comparison of CRQ with other numerical integration softwares.
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Contributor : Laurent Fousse <>
Submitted on : Wednesday, April 28, 2010 - 2:52:28 PM
Last modification on : Tuesday, April 24, 2018 - 1:37:06 PM
Document(s) archivé(s) le : Tuesday, September 28, 2010 - 12:53:34 PM


  • HAL Id : tel-00477243, version 1


Laurent Fousse. Intégration numérique avec erreur bornée en précision arbitraire. Modélisation et simulation. Université Henri Poincaré - Nancy I, 2006. Français. ⟨tel-00477243⟩



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