Comments on the Nature of Automatic Quadrature Routines

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Comments on the Nature of Automatic Quadrature Routines

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ACM Transactions on Mathematical Software (TOMS) archive
Volume 2 , Issue 1 (March 1976) table of contents

Pages: 65 - 81

Year of Publication: 1976

ISSN:0098-3500

Authors

J. N. Lyness	Applied Mathematics Division, Argonne National Laboratory, Argonne, IL
J. J. Kaganove	Apphed Mathematics Divismn, Argonne National Laboratory, Argonne, IL

Publisher

ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 1, Downloads (12 Months): 19, Citation Count: 13

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REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	1	BAaRATT, W. Convergence propertms of Gausslan quadrature formulae. Computer J. 3 (1960), 272-277.
	2	CODY, W.J. The construction of numerical subroutine hbrarms. SIAM Rev. 16 (1974), 36--46.
	3	DE BooR, C. On writing an automatm integration algorithm. In Mathematical Software, J.R. Rice, Ed., Academic Press, New York, 1971, pp. 201-209.
	4	DE BooR, C. CADRE: an algorithm for numerical quadrature. In Mathematical Software, J.R. Rice, Ed., Academic Press, New York, 1971, pp. 417-449.
	5	LYNESS, J.N. The effect of inadequate convergence criteria m automatm routines. Computer J. 12 (1969), 279-281.
	6	O'~-~ARA, I-~., AND SMITH, F.J. The evaluation of definite integrals by interval sub&vision. Computer J. 12 (1969), 179-182.
	7	John R. Rice, A Metalgorithm for Adaptive Quadrature, Journal of the ACM (JACM), v.22 n.1, p.61-82, Jan. 1975 [doi>10.1145/321864.321870]

CITED BY 13

	George Corliss , Gary Krenz, Indefinite integration with validation, ACM Transactions on Mathematical Software (TOMS), v.15 n.4, p.375-393, Dec. 1989
	Marc J. Ouellette , Eugene Fiume, On numerical solutions to one-dimensional integration problems with applications to linear light sources, ACM Transactions on Graphics (TOG), v.20 n.4, p.232-279, October 2001
	Philip E. Gill , Walter Murray , Susan M. Picken , Maragret H. Wright, The Design and Structure of a Fortran Program Library for Optimization, ACM Transactions on Mathematical Software (TOMS), v.5 n.3, p.259-283, Sept. 1979
	F. N. Fritsch , D. K. Kahaner , J. N. Lyness, Double Integration Using One-Dimensional Adaptive Quadrature Routines: A Software Interface Problem, ACM Transactions on Mathematical Software (TOMS), v.7 n.1, p.46-75, March 1981
	Jarle Berntsen , Terje O. Espelid , Alan Genz, An adaptive algorithm for the approximate calculation of multiple integrals, ACM Transactions on Mathematical Software (TOMS), v.17 n.4, p.437-451, Dec. 1991
	Paola Favati , Grazia Lotti , Francesco Romani, Algorithm 691; Improving QUADPACK automatic integration routines, ACM Transactions on Mathematical Software (TOMS), v.17 n.2, p.218-232, June 1991
	Jarle Berntsen , Terje O. Espelid, Algorithm 706; DCUTRI: an algorithm for adaptive cubature over a collection of triangles, ACM Transactions on Mathematical Software (TOMS), v.18 n.3, p.329-342, Sept. 1992
	Jarle Berntsen , Terje O. Espelid, Error estimation in automatic quadrature routines, ACM Transactions on Mathematical Software (TOMS), v.17 n.2, p.233-252, June 1991
	Jarle Berntsen , Ronald Cools , Terje O. Espelid, Algorithm 720; an algorithm for adaptive cubature over a collection of 3-dimensional simplices, ACM Transactions on Mathematical Software (TOMS), v.19 n.3, p.320-332, Sept. 1993
	W. J. Cody, Software basics for computational mathematics, ACM SIGNUM Newsletter, v.15 n.2, p.18-29, June 1980
	J. R. Rice , C. W. Gear , J. Ortega , B. Parlett , M. Schultz , L. F. Shampine , P. Wolfe , J. F. Traub, Numerical computations: its nature and research directions, ACM SIGNUM Newsletter, v.14 n.si-1, p.1-48, February 1979
	Ricolindo L. Cariño , Ioana Banicescu, Dynamic load balancing with adaptive factoring methods in scientific applications, The Journal of Supercomputing, v.44 n.1, p.41-63, April 2008
	F W Zwan, An automatic adaptive integration routine in APL, ACM SIGAPL APL Quote Quad, v.17 n.2, p.21-24, Dec. 1986