toms424
toms424,
a FORTRAN77 code which
implements ACM toms algorithm 424, for ClenshawCurtis
quadrature to estimate the integral of a function F(X) from A to B.
While the text of many ACM toms algorithms is available online
through ACM:
http://www.acm.org/pubs/calgo
or NETLIB:
http://www.netlib.org/toms/index.html, most of the early
algorithms are not available. This is one of them. I typed it
in.
Usage:

quad = CCQUAD(F,A,B,TOLERR,LIMIT,ESTERR,USED,CSXFRM)

returns an estimate of the integral of F(X) from A
to B, with the requested relative accuracy TOLERR,
using no more than LIMIT function evaluations, achieving
an estimated error of ESTERR, and actually using USED
function evaluations. The cosine tranform is returned in
CSXFRM(1:USED).
Licensing:
The computer code and data files described and made available on this web page
are distributed under
the GNU LGPL license.
Languages:
toms424 is available in
a FORTRAN77 version.
Related Programs:
toms424_test
intlib,
a FORTRAN90 library which
estimates integrals.
TEST_INT,
a FORTRAN90 library which
defines many test integrands.
Reference:

Charles Clenshaw, Alan Curtis,
A Method for Numerical Integration on Automatic Computers,
Numerische Mathematik,
Volume 2, Number 1, December 1960, pages 197205.

W Morven Gentleman,
Algorithm 424: ClenshawCurtis Quadrature,
Communications of the ACM,
Volume 15, Number 5, May 1972, pages 353355.
Source Code:
Last revised on 14 November 2023.