Multiple-Precision Correctly rounded Newton-Cotes quadrature
RAIRO - Theoretical Informatics and Applications (2007)
- Volume: 41, Issue: 1, page 103-121
- ISSN: 0988-3754
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topFousse, Laurent. "Multiple-Precision Correctly rounded Newton-Cotes quadrature." RAIRO - Theoretical Informatics and Applications 41.1 (2007): 103-121. <http://eudml.org/doc/250041>.
@article{Fousse2007,
abstract = {
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.
},
author = {Fousse, Laurent},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {numerical integration; correct rounding; multiple-precision;
Newton-Cotes; multiple-precision arithmetic; Newton-Cotes quadrature; roundoff error; error bounds; numerical examples; worst case error analysis},
language = {eng},
month = {4},
number = {1},
pages = {103-121},
publisher = {EDP Sciences},
title = {Multiple-Precision Correctly rounded Newton-Cotes quadrature},
url = {http://eudml.org/doc/250041},
volume = {41},
year = {2007},
}
TY - JOUR
AU - Fousse, Laurent
TI - Multiple-Precision Correctly rounded Newton-Cotes quadrature
JO - RAIRO - Theoretical Informatics and Applications
DA - 2007/4//
PB - EDP Sciences
VL - 41
IS - 1
SP - 103
EP - 121
AB -
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.
LA - eng
KW - numerical integration; correct rounding; multiple-precision;
Newton-Cotes; multiple-precision arithmetic; Newton-Cotes quadrature; roundoff error; error bounds; numerical examples; worst case error analysis
UR - http://eudml.org/doc/250041
ER -
References
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- The Spaces project. The MPFR library, version 2.0.1. (2002). URIhttp://www.mpfr.org/
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