TOMS351
Modified Romberg Quadrature
TOMS351
is a FORTRAN77 library which
implements ACM TOMS algorithm 351, for modified Romberg
quadrature.
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.
Usage:

call romint ( val, err, eps, a, b, n, maxe, f )

where VAL is returned as the estimated integral,
ERR is returned as an error bound for the estimated integral,
EPS is the desired accuracy,
A and B define the interval of integration,
N is the number of function evaluations,
MAXE is the number of extrapolations,
and F is the name of the FORTRAN function that evaluates
the integrand.
Languages:
TOMS351 is available in
a FORTRAN77 version.
Related Data and Programs:
INTLIB,
a FORTRAN90 library which
can estimate the integral of a function.
QUADPACK,
a FORTRAN90 library which
can estimate the integral of a function,
including weight functions, singularities, and infinite intervals.
QUADRULE,
a FORTRAN90 library which
defines many simple quadrature schemes.
STROUD,
a FORTRAN90 library which
defines quadrature schemes for a number of geometrically
interesting regions.
TEST_INT,
a FORTRAN90 library which
contains routines which define integrands suitable for testing
integration software.
TOMS468,
a FORTRAN77 library which
carries out the automatic integration of a function.
Reference:

ND Cook,
Remark on Algorithm 351: Modified Romberg Quadrature,
Communications of the ACM,
April 1970, Volume 13, Issue 4, page 263.

Graeme Fairweather,
Algorithm 351: Modified Romberg Quadrature,
Communications of the ACM,
June 1969, Volume 12, page 324.

George Wallick,
Remark on Algorithm 351: Modified Romberg Quadrature,
Communications of the ACM,
June 1970, Volume 13, Issue 6, page 374376.
Source Code:
Examples and Tests:
List of Routines:

ROMINT estimates an integral using modified Romberg quadrature.
You can go up one level to
the FORTRAN77 source codes.
Last revised on 05 January 2006.