An Experimental Algorithm for N-Dimensional Adaptive Quadrature

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An Experimental Algorithm for N-Dimensional Adaptive Quadrature

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ACM Transactions on Mathematical Software (TOMS) archive
Volume 5 , Issue 1 (March 1979) table of contents

Pages: 86 - 96

Year of Publication: 1979

ISSN:0098-3500

Authors

David K. Kahaner	University of California, Los Alamos Scientific Laboratory, P O Box 1663, Los Alamos, NM
Mark B. Wells	University of California, Los Alamos Scientific Laboratory, P O Box 1663, Los Alamos, NM

Publisher

ACM New York, NY, USA

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Downloads (6 Weeks): 0, Downloads (12 Months): 33, Citation Count: 4

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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	BURGE, W.H. Recursive Programming Techniques. Addison-Wesley, Reading, Mass., 1975.
	2	DE BALBINE, G. Ph D. Th., Califorma Inst Tech, 1968, pp. 149-150.
	3	DE BOOR, C.A. CADRE: An algorithm for numerical quadrature. In Mathematical Software, j.R. Rme, Ed., ACM Mono. Set, ACM, New York, 1971, pp 417-450.
	4	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 [doi>10.1145/355934.355938]
	5	GENZ, A. An adaptive multidnnensional quadrature procedure. Comp Phys. Comm. 4 (1972), 11-15.
	6	KAHANER, D.K., AND WELLS, M B. An algomthm for N-dimensional adaptive quadrature using advanced programming techmques Rep. LA-UR 76-2310, Los Alamos Scl. Lab., Los Alamos, N. Mex., Nov 1976.
	7	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
	8	KUHN, H W. Simphclal approximation of fixed points. Proc. Nat. Acad. Sci. 61 (1968), 1238-1242.
	9	LYNESS, J N An error functmnal expansmn for N-dimensional quadrature with an lntegrand function singular at a point Math. Comput. 30, 133 (Jan 1976), 1-23.
	10	LYNESS, J N. Quadrature over a simplex: pt 1. A representation for the integrand function SIAM J Numer. Anal 15, 1 {Feb. 1978), 122-133.
	11	LYNESS, J.N. Quadrature over a simplex: pt 2. A representation for the error functional. To appear in SIAM J Numer Anal.
	12	LYNESS, J N. The automatic quadrature routine interface. Presented at Los Alamos Workshop on Quadrature Algorithms, Los Alamos, N. Mex., May 1975.
	13	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 [doi>10.1145/355637.355640]
	14	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]
	15	SHAPLEY, L.S. On balanced games without side payments. In Mathematical Programming, Hu and Robinson, Eds., Academic Press, N.Y, 1973.
	16	SILVESTER, P. Symmetric quadrature formula for simplexes. Math. Comput. 24, 109 (1970), 95-100.
	17	WELLS, M.B. Implementation and application of a function data type Proc. AFIPS 1977 NCC, Vol. 46, AFIPS Press, Montvale, N J., pp 389-395
	18	James B. Morris , Mark B. Wells, The specification of program flow in Madcap 6, ACM SIGPLAN Notices, v.7 n.11, November 1972 [doi>10.1145/987361.987366]

CITED BY 4

	Jerome H. Friedman , Margaret H. Wright, A Nested Partitioning Procedure for Numerical Multiple Integration, ACM Transactions on Mathematical Software (TOMS), v.7 n.1, p.76-92, March 1981
	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
	Alan Genz , Ronald Cools, An adaptive numerical cubature algorithm for simplices, ACM Transactions on Mathematical Software (TOMS), v.29 n.3, p.297-308, September 2003
	David K. Kahaner, BASIC for numerical quadrature, ACM SIGNUM Newsletter, v.16 n.2, p.21-24, June 1981