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Schmid, Hans Joachim

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

Numer. Math. 31, 281-297 (1978).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
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Cited in 5 Reviews
Cited in 22 Documents

MSC:

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

Keywords:

minimal number of knots; two-dimensional analogon; Gaussian quadrature problem; cubature formulae; minimal formulae

Citations:

Zbl 0217.147; Zbl 0419.33010
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\textit{H. J. Schmid}, Numer. Math. 31, 281--297 (1978; Zbl 0427.65014)
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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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.