# 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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