1,722,102 research outputs found
Probabilistic Analysis of Simpson′s Quadrature
No full textAbstractWe study probabilistic properties of Simpson′s quadrature, assuming that the class of integrands is equipped with a variant of the r-fold Wiener measure. In the average case setting, we show that the error of Simpson′s quadrature is minimal (modulo a multiplicative constant) when equally spaced points are used. Furthermore, composite Simpson′s quadrature with equally spaced points is almost optimal among all algorithms iff the regularity degree r does not exceed 3. We are also interested in computing a posteriori bounds on the error of Simpson′s quadrature. The error bounds as well as the approximation to ∫10 ƒ(x) dx are computed based on a (fixed) finite number of function values. We derive a new a posteriori error bound for Simpson′s quadrature and show that, from a probabilistic point of view, it is significantly better than a bound that is commonly used in practice
Simpson, S O, 402987
No full textThis record was harvested from a previous catalogue system and will be withdrawn in 2025. Information in this record may be superseded or incomplete. Visit this record in UMA's new catalogue at: https://archives.library.unimelb.edu.au/nodes/view/416956Surname: SIMPSON. Given Name(s) or Initials: S O. Military Service Number or Last Known Location: 402987. Missing, Wounded and Prisoner of War Enquiry Card Index Number: 35128.239530
Item: [2016.0049.49217] "Simpson, S O, 402987
Simpson, S T, TX2188
No full textThis record was harvested from a previous catalogue system and will be withdrawn in 2025. Information in this record may be superseded or incomplete. Visit this record in UMA's new catalogue at: https://archives.library.unimelb.edu.au/nodes/view/417022Surname: SIMPSON. Given Name(s) or Initials: S T. Military Service Number or Last Known Location: TX2188. Missing, Wounded and Prisoner of War Enquiry Card Index Number: 31118.239662
Item: [2016.0049.49283] "Simpson, S T, TX2188
- …
