Local Versus Global Strategies for Adaptive Quadrature

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Local Versus Global Strategies for Adaptive Quadrature

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ACM Transactions on Mathematical Software (TOMS) archive
Volume 1 , Issue 2 (June 1975) table of contents

Pages: 129 - 146

Year of Publication: 1975

ISSN:0098-3500

Authors

Michael A. Malcolm	Department of Computer Science, University of Waterloo, Waterloo, Ont., Canada N2L 3G1
R. Bruce Simpson	Department of Computer Science, University of Waterloo, Waterloo, Ont., Canada N2L 3G1

Publisher

ACM New York, NY, USA

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Downloads (6 Weeks): 4, Downloads (12 Months): 51, Citation Count: 12

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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	DEBOOR, C. CADRE: an algorithm for numerical quadrature, in Mathematical Software, J. Rice, Ed. Academic Press, New York, 1971, pp. 417-449.
	2	FLOYD, R., W. Treesort 3, Algorithm 245. Comm. ACM 7, 12 (Dec. 1964), 701.
	3	Donald E. Knuth, The art of computer programming, volume 3: (2nd ed.) sorting and searching, Addison Wesley Longman Publishing Co., Inc., Redwood City, CA, 1998
	4	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]
	5	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]
	6	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]
	7	T. N. L. Patterson, Algorithm 468: algorithm for automatic numerical integration over a finite interval [D1], Communications of the ACM, v.16 n.11, p.694-699, Nov. 1973 [doi>10.1145/355611.362543]
	8	PIEssENs, R. An algorithm for automatic integration. Angewandte Informatik (Sept. 1973), 399-401.
	9	PIESSENS, R. A quadrature routine with round-off error guard. Rep. TW 17, Appl. Math. and Programming Div., Catholic University of Leuven, Belgium, March 1974.
	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]
	11	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]
	12	ROWLAND, J. H., AND VAROL, Y. L. Exit criteria for Simpson's compound rule. Math. Compu~ ration 26, 119 (July 1972), 699-704.

CITED BY 12

	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
	Jean Vuillemin, A data structure for manipulating priority queues, Communications of the ACM, v.21 n.4, p.309-315, April 1978
	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
	Ian Robinson, An Algorithm for Automatic Integration Over a Triangle Using Nonlinear Extrapolation, ACM Transactions on Mathematical Software (TOMS), v.10 n.1, p.1-16, March 1984
	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
	Gaston H. Gonnet, Heaps applied to event driven mechanisms, Communications of the ACM, v.19 n.7, p.417-418, July 1976
	Elise de Doncker, An adaptive extrapolation algorithm for automatic integration, ACM SIGNUM Newsletter, v.13 n.2, p.12-18, June 1978
	Boris Weissman , Benedict Gomes, High-performance thread migration on clusters of SMPs, Cluster computing, Nova Science Publishers, Inc., Commack, NY, 2001
	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
	Terje O. Espelid, Algorithm 868: Globally doubly adaptive quadrature—reliable Matlab codes, ACM Transactions on Mathematical Software (TOMS), v.33 n.3, p.21-es, August 2007
	Chin-Yun Chen, Bivariate Product Cubature Using Peano Kernels for Local Error Estimates, Journal of Scientific Computing, v.36 n.1, p.69-88, July 2008