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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...
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