Multiple-Precision Correctly rounded Newton-Cotes quadrature
Univ. Nancy I/LORIA,
615 rue du Jardin Botanique, 54602 Villers-lès-Nancy Cedex, France; firstname.lastname@example.org
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.
Mathematics Subject Classification: 65D30 / 65D32 / 65G50
Key words: numerical integration / correct rounding / multiple-precision / Newton-Cotes
© EDP Sciences, 2007