Abstract
Gordon [3], [4] introduced the Boolean method of multivariate interpolation. In the two-dimensional case Delvos-Posdorf [2] considered interpolation projectors which are Boolean sums of R tensor product Lagrange interpolation projectors. In this paper these R-th order projectors are used to construct cubature formulas of interpolatory type. For these cubature formulas we determine the degree of polynomial exactness. As an application the minimum point formulas of Morrow-Patterson [8] are constructed by Boolean methods.
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References
Chawla, M.M.: Error bounds for the Gauss-Chebyshev quadrature formula of the closed type. Math. Comp. 22, 889–891 (1968)
Delvos, F.-J., Posdorf, H.: Boolesche zweidimensionale Lagrange-Interpolation. Computing 22, 311 – 323 (1979)
Gordon, W.J.: Distributive lattices and approximation of multivariate functions. Proc. Symp. Approximations with Special Emphasis on Spline Functions. Ed.: I.J. Schoenberg. Academic Press, 223–277 (1969)
Gordon, W.J.: Blending-function methods of bivariate and multivariate interpolation and approximation. SIAM J. Numer. Anal. 8, 158 – 177 (1971)
Möller, H.M.: Polynomideale und Kubaturformeln. Dissertation, Universität Dortmund (1973)
Möller, H.M.: Kubaturformeln mit minimaler Knotenzahl. Numer. Math. 25, 185–200 (1976)
Monegato, G.: A note on extended Gaussian quadrature rules. Math. Comp. 30, 812–817 (1976)
Morrow, C.R., Patterson, T.N.L.: Construction of algebraic cubature rules using polynomial ideal theory. SIAM J. Numer. Anal. 15, 953–976 (1978)
Neumann, G.: Boolesche interpolatorische Kubatur. Preprint, Universität Siegen (1981)
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Neumann, G. (1982). Boolean Constructed Cubature Formulas of Interpolatory Type. In: Hämmerlin, G. (eds) Numerical Integration. ISNM 57: International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 57. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6308-7_18
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DOI: https://doi.org/10.1007/978-3-0348-6308-7_18
Publisher Name: Birkhäuser, Basel
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