Publication: Adaptive, Self-Validating Numerical Quadrature
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Adaptive, Self-Validating Numerical Quadrature

- Article in a journal -
 

Author(s)
George F. Corliss , Louis B. Rall

Published in
SIAM Journal on Statistical and Scientific Computing

Year
1987

Abstract
Validated bounds for If = _a^b f(x) dx are computed using Gaussian, Newton-Cotes, or Taylor polynomial quadrature. The algorithm uses both subinterval and order adaptation. Results often differ by a few units in the last place.

AD Theory and Techniques
Interval Arithmetic

BibTeX
@ARTICLE{
         Corliss1987ASV,
       author = "George F. Corliss and Louis B. Rall",
       title = "Adaptive, Self-Validating Numerical Quadrature",
       journal = "{SIAM} Journal on Statistical and Scientific Computing",
       volume = "8",
       number = "5",
       year = "1987",
       pages = "831--847",
       referred = "[Rall1996AIt].",
       comment = "Also {\sl MRC Technical Summary Report No. 2815,\/} University of
         Wisconsin-MadGUM1995Gttn, 1985.",
       keywords = "quadrature; automatic differentiation.",
       abstract = "Validated bounds for $ If = \int_a^b f(x)\,dx $ are computed using
         Gaussian, Newton-Cotes, or Taylor polynomial quadrature. The algorithm uses both subinterval and
         order adaptation. Results often differ by a few units in the last place.",
       url = "http://link.aip.org/link/?SCE/8/831/1",
       doi = "10.1137/0908069",
       ad_theotech = "Interval Arithmetic"
}


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