JIPAM logo: Home Link
Home Editors Submissions Reviews Volumes RGMIA About Us

  Volume 3, Issue 4, Article 49
Sharp Error Bounds for the Trapezoidal Rule and Simpson's Rule

    Authors: David Cruz-Uribe, C.J. Neugebauer,  
    Keywords: Numerical integration, Trapezoidal rule, Simpson's rule  
    Date Received: 04/04/02  
    Date Accepted: 01/05/02  
    Subject Codes:


    Editors: Alberto Fiorenza,  

We give error bounds for the trapezoidal rule and Simpson's rule for ``rough'' continuous functions--for instance, functions which are Hölder continuous, of bounded variation, or which are absolutely continuous and whose derivative is in $ L^p$. These differ considerably from the classical results, which require the functions to have continuous higher derivatives. Further, we show that our results are sharp, and in many cases precisely characterize the functions for which equality holds. One consequence of these results is that for rough functions, the error estimates for the trapezoidal rule are better (that is, have smaller constants) than those for Simpson's rule.

  Download Screen PDF
  Download Print PDF
  Send this article to a friend
  Print this page

      search [advanced search] copyright 2003 terms and conditions login