A Metalgorithm for Adaptive Quadrature

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A Metalgorithm for Adaptive Quadrature

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Journal of the ACM (JACM) archive
Volume 22 , Issue 1 (January 1975) table of contents

Pages: 61 - 82

Year of Publication: 1975

ISSN:0004-5411

Author

John R. Rice

Computer Sciences, Mathematical Sciences Building, Purdue University, West Lafayette, IN

Publisher

ACM New York, NY, USA

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Downloads (6 Weeks): 3, Downloads (12 Months): 76, Citation Count: 17

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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	DE Boos, C On writing an automatic integration algorithm. In Mathematical Software, J. R. Rice, Ed, Academm Press, New York, 1971, pp 201-209
	2	DE BOOR, C CADRE. An algorithm for numerical quadrature In Mathematical Software, J. R. Rice, Ed, Academm Press, New York, 1971, Chap 7, pp 417-449
	3	CASALETTO, J, PICKET, M, AND RICE, J A comparison of some numerical integration programs CSD TR 37, Purdue U, Lafayette, ind, June 1969, also SIGNUM Newsletter ~ (1969), 30-40
	4	D~vIs, P, AND RABINOWI~Z, P NumericalIntegration Blaisdell, Waltham, Mass, 1967
	5	KA~ANEa, D. K Comparison of numerical quadrature formulas in Mathematwal Software, J R Rme, Ed, Academic Press, New York, 1971, pp 229-259
	6	KUmK, R Havie integrator, Algorithm 257 Comm ACM 8, 6 (June 1965), 381
	7	J. N. Lyness, Notes on the Adaptive Simpson Quadrature Routine, Journal of the ACM (JACM), v.16 n.3, p.483-495, July 1969 [doi>10.1145/321526.321537]
	8	J. N. Lyness, Algorithm 379: Squank (Simpson Quadrature used adaptivity—noise killed) [D1], Communications of the ACM, v.13 n.4, p.260-262, April 1970 [doi>10.1145/362258.362289]
	9	William Marshall McKeeman, Algorithm 145: Adaptive numerical integration by Simpson's rule, Communications of the ACM, v.5 n.12, p.604, Dec. 1962 [doi>10.1145/355580.369102]
	10	John R. Rice, An educational adaptive quadrature algorithm, ACM SIGNUM Newsletter, v.8 n.2, p.27-41, April 1973 [doi>10.1145/1052641.1052644]

CITED BY 17

	Jarle Berntsen , Terje O. Espelid , Alan Genz, Algorithm 698; DCUHRE: an adaptive multidemensional integration routine for a vector of integrals, ACM Transactions on Mathematical Software (TOMS), v.17 n.4, p.452-456, Dec. 1991
	John R. Rice, Parallel Algorithms for Adaptive Quadrature. III. Program Correctness, ACM Transactions on Mathematical Software (TOMS), v.2 n.1, p.1-30, March 1976
	James R. McGraw, The VAL Language: Description and Analysis, ACM Transactions on Programming Languages and Systems (TOPLAS), v.4 n.1, p.44-82, Jan. 1982
	Elise de Doncker , Ian Robinson, Algorithm 612: TRIEX: Integration Over a TRIangle Using Nonlinear EXtrapolation, ACM Transactions on Mathematical Software (TOMS), v.10 n.1, p.17-22, March 1984
	Michael A. Malcolm , R. Bruce Simpson, Local Versus Global Strategies for Adaptive Quadrature, ACM Transactions on Mathematical Software (TOMS), v.1 n.2, p.129-146, June 1975
	David K. Kahaner , Mark B. Wells, An Experimental Algorithm for N-Dimensional Adaptive Quadrature, ACM Transactions on Mathematical Software (TOMS), v.5 n.1, p.86-96, March 1979
	J. N. Lyness , J. J. Kaganove, Comments on the Nature of Automatic Quadrature Routines, ACM Transactions on Mathematical Software (TOMS), v.2 n.1, p.65-81, March 1976
	J. M. Bull , T. L. Freeman, Parallel algorithms for multi-diemsnional integration, Progress in computer research, Nova Science Publishers, Inc., Commack, NY, 2001
	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
	James M. Lemme , John R. Rice, Speedup in Parallel Algorithms for Adaptive Quadrature, Journal of the ACM (JACM), v.26 n.1, p.65-71, Jan. 1979
	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
	D. P. Laurie, Algorithm 584: CUBTRI: Automatic Cubature over a Triangle, ACM Transactions on Mathematical Software (TOMS), v.8 n.2, p.210-218, June 1982
	Ronald F. Boisvert, Mathematical software: past, present, and future, Computational science, mathematics and software, Purdue University Press, West Lafayette, IN, 2002
	J. M. Bull , T. L. Freeman, Parallel algorithms for multi-diemsnional integration, Progress in computer research, Nova Science Publishers, Inc., Commack, NY, 2001
	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
	Henry D. Shapiro, Increasing robustness in global adaptive quadrature through interval selection heuristics, ACM Transactions on Mathematical Software (TOMS), v.10 n.2, p.117-139, June 1984
	F W Zwan, An automatic adaptive integration routine in APL, ACM SIGAPL APL Quote Quad, v.17 n.2, p.21-24, Dec. 1986