no. 1
Multiple-precision correctly rounded Newton-Cotes quadrature
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 41 (2007) no. 1, pp. 103-121.

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.

DOI : 10.1051/ita:2007004
Classification : 65D30, 65D32, 65G50
Mots clés : numerical integration, correct rounding, multiple-precision, Newton-Cotes 
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     author = {Fousse, Laurent},
     title = {Multiple-precision correctly rounded {Newton-Cotes} quadrature},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {103--121},
     publisher = {EDP-Sciences},
     volume = {41},
     number = {1},
     year = {2007},
     doi = {10.1051/ita:2007004},
     mrnumber = {2330046},
     zbl = {1136.65032},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ita:2007004/}
}
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Fousse, Laurent. Multiple-precision correctly rounded Newton-Cotes quadrature. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 41 (2007) no. 1, pp. 103-121. doi : 10.1051/ita:2007004. http://www.numdam.org/articles/10.1051/ita:2007004/

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