JUCS - Journal of Universal Computer Science 4(1): 2-10, doi: 10.3217/jucs-004-01-0002
Dynamical Control of Computations Using the Trapezoidal and Simpson's Rules
expand article infoJean-Marie Chesneaux‡, Fabienne Jézéquel‡
‡ LIP6 Laboratory, Pierre et Marie Curie University, France

Corresponding author: Jean-Marie Chesneaux ( jean-marie.chesneaux@lip6.fr )

© Jean-Marie Chesneaux, Fabienne Jézéquel.
This article is freely available under the J.UCS Open Content License.
Citation: Chesneaux J-M, Jézéquel F (1998) Dynamical Control of Computations Using the Trapezoidal and Simpson's Rules. JUCS - Journal of Universal Computer Science 4(1): 2-10. https://doi.org/10.3217/jucs-004-01-0002
Open Access
Abstract
If In is the approximation of a definite integral with step using the trapezoidal rule (respectively Simpson's rule), if Ca,b denotes the number of significant digits common to a and b, we show, in this paper, that According to the previous theorems, using the CADNA library which allows on computers to estimate the round-off error effect on any computed result, we can compute dynamically the optimal value of n to approximate I and we are sure that the exact significant digits of In are in common with the significant digits of I.
Keywords
numerical validation, quadrature methods, trapezoidal rule, Simpson's rule