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Generalized Melkes Interpolation

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Multivariate Approximation Theory III

Part of the book series: International Series of Numerical Mathematics ((ISNM,volume 75))

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Abstract

An important class of rectangular finite elements are those of reduced Hermite interpolation type. In comparison with the corresponding tensor product interpolation the number of nodes is reduced; only the values of the function f and its derivatives \(D_x^iD_y^if{\text{ }}\left( {0 \leqslant i + j \leqslant M} \right)\) in the vertices of the given recytangle are used.

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References

  1. Baszenski, G., Delvos, F.J., Posdorf, H., “Representation formulas for conforming bivari ate interpolation”. In: Approximation theory III. Ed. E. W. Cheney, Academic Press (1980), 193 – 198.

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  2. Delvos, F.J., Posdorf, H., “A representation formula for reduced Hermite interpolation”. In: Numeri sche Methoden der Approximationstheorie, Bd. 4. Eds.: L. Collatz, G. Meinardus, H. Werner. ISLAM 42 (1978), 124–137.

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  3. Gordon, W. J., “Distributive lattices and approximation of multivariate functions” Proc. Symp. Madison (Wi sc.) (1969), 223 – 277

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  4. Melkes, F., “Reduced piecewise bivariate Hermite interpolation”. Num. Math. 19 (1972), 326 – 340.

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  5. Phillips, G.M., “Explicit Forms for certain Hermite approximations” BIT 13 (1973), 177 – 180

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© 1985 Birkhäuser Verlag Basel

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Nienhaus, H. (1985). Generalized Melkes Interpolation. In: Schempp, W., Zeller, K. (eds) Multivariate Approximation Theory III. International Series of Numerical Mathematics, vol 75. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9321-3_30

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  • DOI: https://doi.org/10.1007/978-3-0348-9321-3_30

  • Publisher Name: Birkhäuser Basel

  • Print ISBN: 978-3-0348-9995-6

  • Online ISBN: 978-3-0348-9321-3

  • eBook Packages: Springer Book Archive

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