IDEAS home Printed from https://ideas.repec.org/h/spr/spochp/978-1-4419-6594-3_17.html
   My bibliography  Save this book chapter

Towards a General Error Theory of the Trapezoidal Rule

In: Approximation and Computation

Author

Listed:
  • Jörg Waldvogel

    (ETH Zürich)

Abstract

The trapezoidal rule is the method of choice for numerical quadrature of analytic functions over the real line ℝ. Other intervals and slowly decaying integrands may elegantly be handled by means of simple analytic transformations of the integration variable. In the case of an integrand analytic in an open strip containing ℝ the discretization error is exponentially small in the reciprocal step size. If the integrand has singularities arbitrarily close to ℝ, the discretization error is larger and its theory is more complicated. We present examples illustrating possible error laws of the trapezoidal rule.

Suggested Citation

  • Jörg Waldvogel, 2010. "Towards a General Error Theory of the Trapezoidal Rule," Springer Optimization and Its Applications, in: Walter Gautschi & Giuseppe Mastroianni & Themistocles M. Rassias (ed.), Approximation and Computation, pages 267-282, Springer.
    • Handle: RePEc:spr:spochp:978-1-4419-6594-3_17
    DOI: 10.1007/978-1-4419-6594-3_17
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Gongqiu Zhang & Lingfei Li, 2019. "Analysis of Markov Chain Approximation for Option Pricing and Hedging: Grid Design and Convergence Behavior," Operations Research, INFORMS, vol. 67(2), pages 407-427, March.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:spochp:978-1-4419-6594-3_17. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.