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Correctly Rounded Newton-Cotes Quadrature

Laurent Fousse 1
1 SPACES - Solving problems through algebraic computation and efficient software
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : Numerical integration is an important operation for scientific computations. Although the different quadrature methods have been well studied from a mathematical point of view, the analysis of the actual error when performing the quadrature on a computer is often neglected. This step is however required for certified arithmetics. We study the Newton-Cotes quadrature scheme and give enough details on the algorithms and the error bounds to enable software developers to write a correctly-rounded Newton-Cotes quadrature.
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https://hal.inria.fr/inria-00070402
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Submitted on : Friday, May 19, 2006 - 8:23:22 PM
Last modification on : Friday, February 4, 2022 - 3:34:27 AM
Long-term archiving on: : Sunday, April 4, 2010 - 9:07:25 PM

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  • HAL Id : inria-00070402, version 1

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Laurent Fousse. Correctly Rounded Newton-Cotes Quadrature. [Research Report] RR-5605, INRIA. 2005, pp.20. ⟨inria-00070402⟩

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