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Multiple-Precision Correctly rounded Newton-Cotes quadrature

Published online by Cambridge University Press:  24 April 2007

Laurent Fousse
Laurent Fousse*
Affiliation:
Univ. Nancy I/LORIA, 615 rue du Jardin Botanique, 54602 Villers-lès-Nancy Cedex, France; laurent@komite.net
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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 in the context of multiple-precision arithmetic and give enough details on the algorithms and the error bounds to enable software developers to write a Newton-Cotes quadrature with bounded error.

Keywords

numerical integrationcorrect roundingmultiple-precisionNewton-Cotes
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 41 , Issue 1: Real Numbers , January 2007 , pp. 103 - 121
Copyright
© EDP Sciences, 2007

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