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:

1. ND Cook,
   Remark on Algorithm 351: Modified Romberg Quadrature,
   Communications of the ACM,
   April 1970, Volume 13, Issue 4, page 263.
2. Graeme Fairweather,
   Algorithm 351: Modified Romberg Quadrature,
   Communications of the ACM,
   June 1969, Volume 12, page 324.
3. George Wallick,
   Remark on Algorithm 351: Modified Romberg Quadrature,
   Communications of the ACM,
   June 1970, Volume 13, Issue 6, page 374-376.

Source Code:

• toms351.f, the source code.
• toms351.sh, commands to compile the source code.

Examples and Tests:

• toms351_prb.f, a sample calling program.
• toms351_prb.sh, commands to compile and run the sample program.
• toms351_prb_output.txt, the output file.

List of Routines:

• ROMINT estimates an integral using modified Romberg quadrature.

You can go up one level to the FORTRAN77 source codes.