From: kogeddes@scg.math.uwaterloo.ca (Keith Geddes)
Subject: Re: Adaptive double exponential quadrature algorithm
Date: 7 Jul 2001 02:04:54 GMT
Newsgroups: sci.math.symbolic
Summary: Maple's algorithm for numerical integration

In article <3B45CCDA.912F42D5@epfl.ch>,
Roland Rozsnyo  <roland.rozsnyo@epfl.ch> wrote:
>
>Hi,
>
>I am searching for the adaptive double exponential quadrature algorithm
>used in Maple to solve some singular integrals.
>
>If possible I am searching for :
>
>- a complete description of the algorithm
>- some references about the error estimates
>- an independent routine where this algorithm is implemented
>and ready to be compiled and used
>
>Thank you for your help.
>
>Roland Rozsnyo


We give a basic description in our paper

    K.O. Geddes and G.J. Fee,
    Hybrid symbolic-numeric integration in Maple.
    Proceedings of ISSAC'92, P.S. Wang (ed.),
    ACM Press, New York, 1992, pp. 36-41.


A particular paper to which we refer is:

    Hidetosi Takahasi and Masatake Mori,
    Double Exponential Formulas for Numerical Integration.
    Publ. Res. Inst. Math. Sci., no. 9, (1974) pages 721-741.
    (Old Journal name:  Publ. RIMS Kyoto Univ.)


-----------------------------------------------
Professor Keith Geddes
Symbolic Computation Group
Department of Computer Science
University of Waterloo
Waterloo  ON  N2L 3G1
CANADA

E-mail: kogeddes@scg.math.uwaterloo.ca
URL:    http://www.scg.uwaterloo.ca/~kogeddes
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