Multiple-precision correctly rounded Newton-Cotes quadrature
Fousse, Laurent
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 41 (2007), p. 103-121 / Harvested from Numdam
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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 developers to write a Newton-Cotes quadrature with bounded error.

Publié le : 2007-01-01
DOI : https://doi.org/10.1051/ita:2007004
Classification:  65D30,  65D32,  65G50 
@article{ITA_2007__41_1_103_0,
     author = {Fousse, Laurent},
     title = {Multiple-precision correctly rounded Newton-Cotes quadrature},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     volume = {41},
     year = {2007},
     pages = {103-121},
     doi = {10.1051/ita:2007004},
     mrnumber = {2330046},
     zbl = {1136.65032},
     language = {en},
     url = {http://dml.mathdoc.fr/item/ITA_2007__41_1_103_0}
}

Fousse, Laurent. Multiple-precision correctly rounded Newton-Cotes quadrature. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 41 (2007) pp. 103-121. doi : 10.1051/ita:2007004. http://gdmltest.u-ga.fr/item/ITA_2007__41_1_103_0/

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