Optimal addition of knots to cubature formulae for planar regions

Ronald Cools1, Anny Haegemans1
1Department of Computer Science, University of Leuven, Heverlee, Belgium

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Tài liệu tham khảo

Cools, R., Haegemans, A.: Construction of fully symmetric cubature formulae of degree 4k?3 for fully symmetric planar regions. Report TW71, K.U. Leuven 1985

Cools, R., Haegemans, A.: Tables of degree 2k?1/2k+1 pairs of cubature formulae for symmetric planar regions, obtained by optimal addition of knots. Report TW76, K.U. Leuven 1986

Haegemans, A.: Tables of symmetrical cubature formulas for the two-dimensional hexagon. Report TW28, K.U. Leuven 1976

Haegemans, A., Piessens, P.: Construction of cubature formulas of degree eleven for symmetric planar regions, using orthogonal polynomials. Numer. Math.25, 139?148 (1976)

Haegemans, A., Piessens, R.: Construction of cubature formulas of degree seven and nine for symmetric planar regions, using orthogonal polynomials. SIAM J. Numer. Anal.14, 492?508 (1977)

M�ller, H.M.: Polynomials und Kubaturformeln, Dissertation, Universit�t Dortmund 1973

M�ller, H.M.: Kubaturformeln mit minimaler Knotenzahl. Numer. Math.25, 185?200 (1976)

Patterson, T.N.L.: The optimum addition of points to quadrature formulae. Math. Comput.22, 847?856 (1968)

Stroud, A.H.: Approximate calculation of multiple integrals, Englewood Cliffs, N.J.: Prentice Hall 1971