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On cubature formulae with a minimal number of knots. (English) Zbl 0427.65014


MSC:

65D32 Numerical quadrature and cubature formulas
41A55 Approximate quadratures
41A63 Multidimensional problems
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References:

[1] Fritsch, F.N.: On the existence of regions with minimal third degree integration formulas. Math. Comput.24, 855-861 (1970) · Zbl 0222.65026
[2] Möller, H.M.: Kubaturformeln mit minimaler Knotenzahl. Numer. Math.25, 185-200 (1976) · Zbl 0319.65019
[3] Mysovskikh, I.P.: On the construction of cubature formulas for the simplest regions [in Russ.]. ?. Vy?isl. Mat. i Mat. Fiz.4, 3-14 (1964)
[4] Mysovskikh, I.P.: On the construction of cubature formulas with fewest nodes. Soviet Math. Dokl.9, 277-280 (1968) · Zbl 0176.14404
[5] Mysovskikh, I.P.: Numerical characteristics of orthogonal polynomials in two variables [in Russ.]. Vestnik Leningrad Univ. Math.19, 46-53 (1970)
[6] Mysovskikh, I.P.: Orthogonal polynomials in several variables [in Russ.]. Metody Vy?isl.10, zdvo Len. Univ. 26-35 (1976) · Zbl 0419.33010
[7] Radon, J.: Zur mechanischen Kubatur. Monatsh. Math.52, 286-300 (1948) · Zbl 0031.31504
[8] Risler, J.J.: Unc charactérisation des idéaux des variétés algébriques réelles. Note aux CRAS. Paris271, 1171-1173 (1970)
[9] Stroud, A.H.: Approximate calculation of multiple integrals. Englewood Cliffs, New Jersey: Prentice Hall 1971 · Zbl 0379.65013
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