intlib
intlib,
a FORTRAN90 code which
estimates integrals over 1D regions.
The integrand may be available as a function F(X), or as data
at equally spaced or unequally spaced points.
Licensing:
The computer code and data files described and made available on this web page
are distributed under
the MIT license
Languages:
intlib is available in
a FORTRAN90 version.
Related Data and Programs:
intlib_test
NINTLIB,
a FORTRAN90 code which
estimates integrals over multidimensional regions.
PRODUCT_RULE,
a FORTRAN90 code which
constructs a product quadrature rule from 1D factor rules.
QUADRATURE_RULES,
a dataset directory which
contains files that define quadrature rules over various 1D intervals
or multidimensional hypercubes.
QUADPACK,
a FORTRAN90 code which
numerically estimates integrals.
QUADRULE,
a FORTRAN90 code which
defines quadrature rules for 1D domains.
STROUD,
a FORTRAN90 code which
defines quadrature rules for a variety of multidimensional reqions.
TEST_INT,
a FORTRAN90 code which
defines test integrands for 1D quadrature rules.
TEST_INT_2D,
a FORTRAN90 code which
defines test integrands for 2D quadrature rules.
Reference:
-
Milton Abramowitz, Irene Stegun,
Handbook of Mathematical Functions,
National Bureau of Standards, 1964,
ISBN: 0-486-61272-4,
LC: QA47.A34.
-
Roland Bulirsch, Josef Stoer,
Fehlerabschaetzungen und Extrapolation mit rationaled Funktionen
bei Verfahren vom Richardson-Typus,
(Error estimates and extrapolation with rational functions
in processes of Richardson type),
Numerische Mathematik,
Volume 6, Number 1, December 1964, pages 413-427.
-
Stephen Chase, Lloyd Fosdick,
An Algorithm for Filon Quadrature,
Communications of the Association for Computing Machinery,
Volume 12, Number 8, August 1969, pages 453-457.
-
Stephen Chase, Lloyd Fosdick,
Algorithm 353:
Filon Quadrature,
Communications of the Association for Computing Machinery,
Volume 12, Number 8, August 1969, pages 457-458.
-
William Cody,
An Overview of Software Development for Special Functions,
in Numerical Analysis Dundee, 1975,
edited by GA Watson,
Lecture Notes in Mathematics, 506,
Springer, 1976.
-
Philip Davis, Philip Rabinowitz,
Methods of Numerical Integration,
Second Edition,
Dover, 2007,
ISBN: 0486453391,
LC: QA299.3.D28.
-
Carl deBoor, John Rice,
CADRE: An algorithm for numerical quadrature,
in Mathematical Software,
edited by John Rice,
Academic Press, 1971,
ISBN: 012587250X,
LC: QA1.M766.
-
Augustin Dubrulle,
A short note on the implicit QL algorithm for symmetric
tridiagonal matrices,
Numerische Mathematik,
Volume 15, Number 5, September 1970, page 450.
-
Philip Gill, GF Miller,
An algorithm for the integration of unequally spaced data,
The Computer Journal,
Number 15, Number 1, 1972, pages 80-83.
-
Gene Golub,
Some Modified Matrix Eigenvalue Problems,
SIAM Review,
Volume 15, Number 2, Part 1, April 1973, pages 318-334.
-
Gene Golub, John Welsch,
Calculation of Gaussian Quadrature Rules,
Mathematics of Computation,
Volume 23, Number 106, April 1969, pages 221-230.
-
John Hart, Ward Cheney, Charles Lawson, Hans Maehly,
Charles Mesztenyi, John Rice, Henry Thatcher,
Christoph Witzgall,
Computer Approximations,
Wiley, 1968.
-
Tore Havie,
On a Modification of the Clenshaw Curtis Quadrature Rule,
BIT,
Volume 9, Number 4, December 1969, pages 338-350.
-
Paul Hennion,
Algorithm 77:
Interpolation, Differentiation and Integration,
Communications of the ACM,
Volume 5, 1962, page 96.
-
Robert Kubik,
Algorithm 257:
Havie Integrator,
Communications of the ACM,
Volume 8, Number 6, June 1965, page 381.
-
James Lyness,
Algorithm 379:
SQUANK (Simpson Quadrature Used Adaptively
- Noise Killed),
Communications of the ACM,
Volume 13, Number 4, April 1970, pages 260-263.
-
Roger Martin, James Wilkinson,
The Implicit QL Algorithm,
Numerische Mathematik,
Volume 12, Number 5, December 1968, pages 377-383.
-
William McKeeman, Lawrence Tesler,
Algorithm 182:
Nonrecursive adaptive integration,
Communications of the ACM,
Volume 6, 1963, page 315.
-
Arthur Stroud, Don Secrest,
Gaussian Quadrature Formulas,
Prentice Hall, 1966,
LC: QA299.4G3S7.
-
James Wilkinson, Christian Reinsch,
Handbook for Automatic Computation,
Volume II, Linear Algebra, Part 2,
Springer, 1971,
ISBN: 0387054146.
Source Code:
Last revised on 18 July 2020.