Multiple-precision correctly rounded Newton-Cotes quadrature

Fousse, Laurent

doi:10.1051/ita:2007004

Fousse, Laurent

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 41 (2007) no. 1, pp. 103-121.

Voir la notice de l'article dans Numdam

Résumé

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.

MR Zbl

DOI : 10.1051/ita:2007004

Classification : 65D30, 65D32, 65G50
Mots-clés : numerical integration, correct rounding, multiple-precision, Newton-Cotes

@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},
     pages = {103--121},
     publisher = {EDP-Sciences},
     volume = {41},
     number = {1},
     year = {2007},
     doi = {10.1051/ita:2007004},
     zbl = {1136.65032},
     mrnumber = {2330046},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/articles/10.1051/ita:2007004/}
}

TY  - JOUR
AU  - Fousse, Laurent
TI  - Multiple-precision correctly rounded Newton-Cotes quadrature
JO  - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY  - 2007
SP  - 103
EP  - 121
VL  - 41
IS  - 1
PB  - EDP-Sciences
UR  - https://geodesic-test.mathdoc.fr/articles/10.1051/ita:2007004/
DO  - 10.1051/ita:2007004
LA  - en
ID  - ITA_2007__41_1_103_0
ER  -

%0 Journal Article
%A Fousse, Laurent
%T Multiple-precision correctly rounded Newton-Cotes quadrature
%J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
%D 2007
%P 103-121
%V 41
%N 1
%I EDP-Sciences
%U https://geodesic-test.mathdoc.fr/articles/10.1051/ita:2007004/
%R 10.1051/ita:2007004
%G en
%F 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) no. 1, pp. 103-121. doi : 10.1051/ita:2007004. https://geodesic-test.mathdoc.fr/articles/10.1051/ita:2007004/

Cité par Sources :