메뉴 건너뛰기




Volumn 7, Issue 3, 2000, Pages 477-485

A survey of known and new cubature formulas for the unit disk

Author keywords

Cubature formulas; Multidimensional integration Rules

Indexed keywords

SURVEYS;

EID: 84906240525     PISSN: 15985865     EISSN: None     Source Type: Journal    
DOI: 10.1007/bf03012263     Document Type: Review
Times cited : (25)

References (28)
  • 1
    • 85011494605 scopus 로고    scopus 로고
    • Constructing cubature formulae: The science behind the art
    • Cambridge University Press
    • R. Cools, Constructing cubature formulae: the science behind the art, Acta Numerica 6, Cambridge University Press (1997), 1-54.
    • (1997) Acta Numerica , vol.6 , pp. 1-54
    • Cools, R.1
  • 2
    • 0033322064 scopus 로고    scopus 로고
    • Monomial cubature rules since "Stroud": A compilation-part 2
    • R. Cools, Monomial cubature rules since "Stroud": a compilation-part 2, J. Comput. Appl. Math. 112, 1-2 (1999), 21-27.
    • (1999) J. Comput. Appl. Math. , vol.112 , Issue.1-2 , pp. 21-27
    • Cools, R.1
  • 3
    • 84906277567 scopus 로고
    • Construction of fully symmetric cubature formulae of degree 4k ? 3 for fully symmetric planar regions
    • Dept. of Computer Science, K.U.Leuven
    • R. Cools and A. Haegemans, Construction of fully symmetric cubature formulae of degree 4k ? 3 for fully symmetric planar regions, Report TW 71, Dept. of Computer Science, K.U.Leuven, 1985.
    • (1985) Report TW 71
    • Cools, R.1    Haegemans, A.2
  • 4
    • 84906225095 scopus 로고
    • Automatic computation of knots and weights of cubature formulae for circular symmetric planar regions
    • Dept. of Computer Science, K.U.Leuven
    • R. Cools and A. Haegemans, Automatic computation of knots and weights of cubature formulae for circular symmetric planar regions, Report TW 77, Dept. of Computer Science, K.U.Leuven, 1986.
    • (1986) Report TW 77
    • Cools, R.1    Haegemans, A.2
  • 5
    • 84906214427 scopus 로고
    • Tables of degree 2k ?1/2k+1 pairs of cubature formulae for symmetric planar regions, obtained by optimal addition of knots
    • Dept. of Computer Science, K.U.Leuven
    • R. Cools and A. Haegemans, Tables of degree 2k ?1/2k+1 pairs of cubature formulae for symmetric planar regions, obtained by optimal addition of knots, Report TW 76, Dept. of Computer Science, K.U.Leuven, 1986.
    • (1986) Report TW 76
    • Cools, R.1    Haegemans, A.2
  • 6
    • 0022813006 scopus 로고
    • Automatic computation of knots and weights of cubature formulae for circular symmetric planar regions
    • R. Cools and A. Haegemans, Automatic computation of knots and weights of cubature formulae for circular symmetric planar regions, J. Comput. Appl. Math. 20 (1987), 153-158.
    • (1987) J. Comput. Appl. Math. , vol.20 , pp. 153-158
    • Cools, R.1    Haegemans, A.2
  • 7
    • 0023287816 scopus 로고
    • Construction of fully symmetric cubature formulae of degree 4k ? 3 for fully symmetric planar regions
    • R. Cools and A. Haegemans, Construction of fully symmetric cubature formulae of degree 4k ? 3 for fully symmetric planar regions, J. Comput. Appl. Math. 17 (1987), 173-180.
    • (1987) J. Comput. Appl. Math. , vol.17 , pp. 173-180
    • Cools, R.1    Haegemans, A.2
  • 8
    • 84906255814 scopus 로고
    • Construction of sequences of embedded cubature formulae for circular symmetric planar regions
    • P. Keast and G. Fairweather, Eds., Reidel Publ. Comp., Dordrecht
    • R. Cools and A. Haegemans, Construction of sequences of embedded cubature formulae for circular symmetric planar regions, In Numerical Integration, P. Keast and G. Fairweather, Eds., Reidel Publ. Comp., Dordrecht (1987), 165-172.
    • (1987) Numerical Integration , pp. 165-172
    • Cools, R.1    Haegemans, A.2
  • 9
    • 0040687299 scopus 로고
    • Construction of symmetric cubature formulae with the number of knots (almost) equal to Möller's lower bound
    • H. Brass and G. Hämmerlin, Eds., Birkhäuser Verlag, Basel
    • R. Cools and A. Haegemans, Construction of symmetric cubature formulae with the number of knots (almost) equal to Möller's lower bound, In Numerical Integration III , H. Brass and G. Hämmerlin, Eds., Birkhäuser Verlag, Basel (1988), 25-36.
    • (1988) Numerical Integration III , pp. 25-36
    • Cools, R.1    Haegemans, A.2
  • 10
    • 0001415473 scopus 로고
    • Monomial cubature rules since 'Stroud': A compilation
    • R. Cools and P. Rabinowitz, Monomial cubature rules since 'Stroud': A compilation, J. Comput. Appl. Math. 48 (1993), 309-326.
    • (1993) J. Comput. Appl. Math. , vol.48 , pp. 309-326
    • Cools, R.1    Rabinowitz, P.2
  • 11
    • 15744403283 scopus 로고
    • Cubature rules with equal coefficients for integrating functions with respect to symmetric domains
    • (Russian)
    • L. Dobrodeev, Cubature rules with equal coefficients for integrating functions with respect to symmetric domains, Zh. vychisl.Mat. mat. Fiz. 18 (1978), 846-852 (Russian).
    • (1978) Zh. Vychisl.Mat. Mat. Fiz. , vol.18 , pp. 846-852
    • Dobrodeev, L.1
  • 13
    • 84906235635 scopus 로고
    • Über gleichgewichtete Kubaturformeln für Kreis- und Sechseck-Gebiet
    • H. Engels, Über gleichgewichtete Kubaturformeln für Kreis- und Sechseck-Gebiet, Elek. Daten. 5 (1970), 216-223.
    • (1970) Elek. Daten. , vol.5 , pp. 216-223
    • Engels, H.1
  • 15
    • 84906221441 scopus 로고
    • Tables of circularly symmetrical integration formulas of degree 2d ? 1 for two-dimensional circularly symmetrical regions
    • K. U. Leuven Applied Mathematics and Programming Division
    • A. Haegemans, Tables of circularly symmetrical integration formulas of degree 2d ? 1 for two-dimensional circularly symmetrical regions, Report TW 27, K.U.Leuven Applied Mathematics and Programming Division, 1975.
    • (1975) Report TW 27
    • Haegemans, A.1
  • 16
    • 0038909480 scopus 로고
    • Construction of cubature formulas of degree eleven for symmetric planar regions, using orthogonal polynomials
    • A. Haegemans and R. Piessens, Construction of cubature formulas of degree eleven for symmetric planar regions, using orthogonal polynomials, Numer. Math. 25 (1976), 139-148.
    • (1976) Numer. Math. , vol.25 , pp. 139-148
    • Haegemans, A.1    Piessens, R.2
  • 17
    • 0040687298 scopus 로고
    • Construction of cubature formulas of degree seven and nine symmetric planar regions using orthogonal polynomials
    • A. Haegemans and R. Piessens, Construction of cubature formulas of degree seven and nine symmetric planar regions, using orthogonal polynomials, SIAM J. Numer. Anal. 14 (1977), 492-508.
    • (1977) SIAM J. Numer. Anal. , vol.14 , pp. 492-508
    • Haegemans, A.1    Piessens, R.2
  • 18
    • 0039022129 scopus 로고    scopus 로고
    • Symmetric quadrature formulas over a unit disk
    • K. Kim and M. Song, Symmetric quadrature formulas over a unit disk, Korean J. Comput. Appl. Math. 4, 1 (1997), 179-192.
    • (1997) Korean J. Comput. Appl. Math. , vol.4 , Issue.1 , pp. 179-192
    • Kim, K.1    Song, M.2
  • 19
    • 84906223641 scopus 로고
    • Numerical location of nodes and weights in a sixthorder quadrature formula for a disk
    • 151-152 (Russian)
    • S. Konyaev and L. Tolmacheva, Numerical location of nodes and weights in a sixthorder quadrature formula for a disk, Voprosy Vychisl. i Prikl. Mat. (Tashkent) 86 (1989), 59-63, 151-152 (Russian).
    • (1989) Voprosy Vychisl. i Prikl. Mat. (Tashkent) , vol.86 , pp. 59-63
    • Konyaev, S.1    Tolmacheva, L.2
  • 22
    • 0016515707 scopus 로고
    • Cubature formulas of degree eleven for symmetric planar regions
    • R. Piessens and A. Haegemans, Cubature formulas of degree eleven for symmetric planar regions, J. Comput. Appl. Math. 1, 2 (1975), 79-83.
    • (1975) J. Comput. Appl. Math. , vol.1 , Issue.2 , pp. 79-83
    • Piessens, R.1    Haegemans, A.2
  • 23
    • 0040093790 scopus 로고
    • Cubature formulas of degree nine for symmetric planar regions
    • R. Piessens and A. Haegemans, Cubature formulas of degree nine for symmetric planar regions, Math. Comp. 29 (1975), 810-815.
    • (1975) Math. Comp. , vol.29 , pp. 810-815
    • Piessens, R.1    Haegemans, A.2
  • 24
    • 33645604871 scopus 로고
    • Construction of cubature formulas containing preassigned nodes
    • (Russian)
    • G. Rasputin, Construction of cubature formulas containing preassigned nodes, Izv. Vyssh. Uchebn. Zaved. Mat. 11 (1986), 44-51 (Russian).
    • (1986) Izv. Vyssh. Uchebn. Zaved. Mat. , vol.11 , pp. 44-51
    • Rasputin, G.1
  • 25
    • 84906237076 scopus 로고
    • (English)
    • Soviet Math. (Iz. VUZ) 30 (1986), 58-67 (English).
    • (1986) Soviet Math. (Iz. VUZ) , vol.30 , pp. 58-67
  • 28
    • 0022734980 scopus 로고
    • Partially symmetric cubature formulas for even degrees of exactness
    • J. W. Wissman and T. Becker, Partially symmetric cubature formulas for even degrees of exactness, SIAM J. Numer. Anal. 23 (1986), 676-685.
    • (1986) SIAM J. Numer. Anal. , vol.23 , pp. 676-685
    • Wissman, J.W.1    Becker, T.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.