Estimating the error in tanh-sinh integration

Discussion in 'Numerical Analysis' started by Toby.Kelsey, Mar 19, 2008.

  1. Toby.Kelsey

    Toby.Kelsey Guest

    I have coded a tanh-sinh quadrature routine (source at
    <http://www.codecodex.com/wiki/index.php?
    title=Numerical_integration_with_tanh-sinh_quadrature>)
    which works, but the estimated error (from the last term) is not very
    accurate.

    I could try improving the error estimate by estimating the limit of
    successive approximations,
    but is there a more direct way of determining the error?

    Toby
     
    Toby.Kelsey, Mar 19, 2008
    #1
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  2. Toby.Kelsey

    user923005 Guest

    Arprec by Bailey:
    http://crd.lbl.gov/~dhbailey/mpdist/
    Has a tool called quad-ts.cpp in the tests folder.
    It performs tanh-sinh quadrature in multiple precision and creates an
    accurate error estimate.
    There are also some excellent papers by Bailey on the subject of tanh/
    sinh quadrature. See:
    http://www.google.com/search?source...,GGLJ:en&q=arprec+bailey+tanh+sinh+quadrature
     
    user923005, Mar 19, 2008
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  3. Toby.Kelsey

    Toby.Kelsey Guest

    Toby.Kelsey, Mar 19, 2008
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