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Volumn 43, Issue 2, 2003, Pages 319-337

Doubly adaptive quadrature routines based on Newton-Cotes rules

Author keywords

Adaptive quadrature; Error estimation; Newton Cotes rules; Software

Indexed keywords


EID: 4043089116     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1026087703168     Document Type: Article
Times cited : (25)

References (22)
  • 1
    • 1542673691 scopus 로고
    • A test of some well known quadrature routines
    • Dept. of Informatics, Univ. of Bergen, Norway
    • J. Berntsen, A test of some well known quadrature routines, Reports in Informatics 20, Dept. of Informatics, Univ. of Bergen, Norway, 1986.
    • (1986) Reports in Informatics 20
    • Berntsen, J.1
  • 2
    • 0026167254 scopus 로고
    • Error estimation in automatic quadrature routines
    • J. Berntsen and T. O. Espelid, Error estimation in automatic quadrature routines, ACM Trans. Math. Software, 17 (1991), pp. 233-252.
    • (1991) ACM Trans. Math. Software , vol.17 , pp. 233-252
    • Berntsen, J.1    Espelid, T.O.2
  • 4
    • 0026303073 scopus 로고
    • An adaptive algorithm for the approximate calculation of multiple integrals
    • J. Berntsen, T. O. Espelid, and A. Genz, An adaptive algorithm for the approximate calculation of multiple integrals, ACM Trans. Math. Software, 17 (1991), pp. 437-451.
    • (1991) ACM Trans. Math. Software , vol.17 , pp. 437-451
    • Berntsen, J.1    Espelid, T.O.2    Genz, A.3
  • 5
    • 0042399479 scopus 로고
    • Cubpack: Progress report
    • T. O. Espelid and A. Genz, eds., NATO ASI Series C: Math. and Phys. Sciences, Kluwer Academic Publishers, Dordrecht
    • R. Cools and A. Haegemans, Cubpack: Progress report, in Numerical Integration, Recent Developments, Software and Applications, T. O. Espelid and A. Genz, eds., NATO ASI Series C: Math. and Phys. Sciences, Kluwer Academic Publishers, Dordrecht, 1992, pp. 305-315.
    • (1992) Numerical Integration, Recent Developments, Software and Applications , vol.357 , pp. 305-315
    • Cools, R.1    Haegemans, A.2
  • 6
    • 0005194244 scopus 로고
    • On writing an automatic integration algorithm
    • J. R. Rice, ed., Academic Press
    • C. de Boor, On writing an automatic integration algorithm, in Mathematical Software, J. R. Rice, ed., Academic Press, 1971.
    • (1971) Mathematical Software
    • De Boor, C.1
  • 8
    • 4043160243 scopus 로고    scopus 로고
    • Doubly adaptive quadrature routines based on Newton-Cotes rules
    • Dept. of Informatics, Univ. of Bergen, Norway
    • T. O. Espelid, Doubly Adaptive Quadrature Routines based on Newton-Cotes rules, Reports in Informatics 229, Dept. of Informatics, Univ. of Bergen, Norway, 2002.
    • (2002) Reports in Informatics 229
    • Espelid, T.O.1
  • 9
    • 0040743052 scopus 로고
    • A discussion of a new error estimate for adaptive quadrature
    • T. O. Espelid and T. Sørevik, A discussion of a new error estimate for adaptive quadrature, BIT, 29 (1989), pp. 283-294.
    • (1989) BIT , vol.29 , pp. 283-294
    • Espelid, T.O.1    Sørevik, T.2
  • 11
    • 0037823843 scopus 로고    scopus 로고
    • Adaptive quadrature - Revisited
    • G. Gander and W. Gautschi, Adaptive quadrature - revisited, BIT, 40 (2000), pp. 84-101.
    • (2000) BIT , vol.40 , pp. 84-101
    • Gander, G.1    Gautschi, W.2
  • 12
    • 0018055904 scopus 로고
    • Algorithm 36 - SNIFF: Efficient self-tuning algorithm for numerical integration
    • S. Garriba, L. Quartapelle, and G. Reina, Algorithm 36 - SNIFF: Efficient self-tuning algorithm for numerical integration, Computing, 20 (1978), pp. 363-375.
    • (1978) Computing , vol.20 , pp. 363-375
    • Garriba, S.1    Quartapelle, L.2    Reina, G.3
  • 13
    • 84976821043 scopus 로고
    • An adaptive algorithm for numerical integration over an N-dimensional rectangular region
    • A. Genz and A. Malik, An adaptive algorithm for numerical integration over an N-dimensional rectangular region, J. Comput. Appl. Math., 6 (1980), pp. 295-302.
    • (1980) J. Comput. Appl. Math. , vol.6 , pp. 295-302
    • Genz, A.1    Malik, A.2
  • 15
    • 0042900392 scopus 로고
    • Comparison of numerical quadrature formulas
    • J. Rice, ed., Academic Press, New York
    • D. Kahaner, Comparison of numerical quadrature formulas, in Mathematical Software, J. Rice, ed., Academic Press, New York, 1971, pp. 229-259.
    • (1971) Mathematical Software , pp. 229-259
    • Kahaner, D.1
  • 16
    • 84968489615 scopus 로고
    • Symmetric integration rules for hypercubes III. Construction of integration rules using null rules
    • J. Lyness, Symmetric integration rules for hypercubes III. Construction of integration rules using null rules, Math. Comp., 19 (1965), pp. 625-637.
    • (1965) Math. Comp. , vol.19 , pp. 625-637
    • Lyness, J.1
  • 17
    • 0016930848 scopus 로고
    • Comments on the nature of automatic quadrature routines
    • J. Lyness and J. Kaganove, Comments on the nature of automatic quadrature routines, ACM Trans. Math. Software, 2 (1976), pp. 65-81.
    • (1976) ACM Trans. Math. Software , vol.2 , pp. 65-81
    • Lyness, J.1    Kaganove, J.2
  • 18
    • 4043113830 scopus 로고
    • A technique for comparing automatic quadrature routines
    • J. Lyness and J. Kaganove, A technique for comparing automatic quadrature routines, Comput. J., 20 (1977), pp. 170-177.
    • (1977) Comput. J. , vol.20 , pp. 170-177
    • Lyness, J.1    Kaganove, J.2
  • 19
    • 4043083845 scopus 로고
    • Algorithm 145. Adaptive numerical integration by Simpson's rule
    • W. M. McKeeman, Algorithm 145. Adaptive numerical integration by Simpson's rule, Comm. ACM, 5 (1962), p. 604.
    • (1962) Comm. ACM , vol.5 , pp. 604
    • McKeeman, W.M.1
  • 21
    • 4043163090 scopus 로고
    • Thesis for the degree Doctor Scientiarum, Department of Informatics, University of Bergen, Norway
    • T. Sørevik, Reliable and Efficient Algorithms for Adaptive Quadrature, Thesis for the degree Doctor Scientiarum, Department of Informatics, University of Bergen, Norway, 1988.
    • (1988) Reliable and Efficient Algorithms for Adaptive Quadrature
    • Sørevik, T.1
  • 22
    • 8344249623 scopus 로고
    • An adaptive algorithm for numerical integration over an N-dimensional cube
    • P. van Dooren and L. de Ridder, An adaptive algorithm for numerical integration over an N-dimensional cube, J. Comput. Appl. Math., 2 (1976), pp. 207-217.
    • (1976) J. Comput. Appl. Math. , vol.2 , pp. 207-217
    • Van Dooren, P.1    De Ridder, L.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.