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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 amathematical point of view, the analysis of the actual error when performingthe quadrature on a computer is often neglected. This step is however requiredfor certified arithmetics.
We study the Newton-Cotes quadrature scheme in the context ofmultiple-precision arithmetic and give enough details on thealgorithms and the error bounds to enable software developers to write aNewton-Cotes quadrature with bounded error.

Keywords

numerical integrationcorrect roundingmultiple-precisionNewton-Cotes

Information

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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