Biermann interpolation of Birkhoff type

Authors

  • Marius Birou Cluj-Napoca, Romania

DOI:

https://doi.org/10.33993/jnaat341-789

Keywords:

Biermann interpolation, Birkhoff interpolation, chains of projectors, approximation order
Abstract views: 174

Abstract

If \(P_{0},P_{1},...,P_{r}\) and \(Q_{0},Q_{1},...,Q_{r}\) are Birkhoff univariate projectors which form the chains\[P_{0}\le P_{1}\le\dots\le P_{r},\quad Q_{0}\le Q_{1}\le\dots\le Q_{r},\]we can define the Biermann operator of Birkhoff type\[B_{r}^{B}=P_{0}^{\prime}Q_{r}^{\prime\prime}\oplus P_{1}^{\prime}Q_{r-1}^{\prime\prime}\oplus\dots\oplus P_{r}^{\prime}Q_{0}^{\prime\prime},\]where \(P_{1}^{\prime},\dots,P_{r}^{\prime}\),\(Q_{1}^{\prime\prime},\dots ,Q_{r}^{\prime\prime}\) are the parametric extension. We give the representations of Biermann interpolant of Birkhoff type for two particular cases (Abel-Goncharov and Lidstone projectors) and we calculate the approximation order of Biermann interpolant in these cases.

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References

Agarwal, R., Wong, P.J.Y., Error inegalities in polynomial interpolation and their applications, Kluwer Academic Publishers, Dordrecht, 1993, https://doi.org/10.1007/978-94-011-2026-5 DOI: https://doi.org/10.1007/978-94-011-2026-5_5

Biermann, O., Uber naherungsweise Cubaturen, Monatshefte fur Mathematik und Physic, 14, pp. 211-225, 1903, https://doi.org/10.1007/bf01706869 DOI: https://doi.org/10.1007/BF01706869

Coman, Gh., Multivariate approximation schemes and the approximation of linear functionals, Rev. Anal. Numér. Théor. Approx. - Mathematica, 16, pp. 229-249, 1974.

Coman, Gh. and all, Interpolation operators, Casa Cărţii de Ştiinţă, 2004.

Davis, Ph. J., Interpolation and approximation, Blaisdell Publishing Company, New york, 1963.

Delvos, F.-J. and Schempp, W., Boolean methods in interpolation and approximation, Pitman Research Notes in Mathematics, Series 230, New York 1989.

Delvos, F.-J. and Posdorf, H., Generalized Biermann interpolation, Resultate Math., 5, no. 1, pp. 6-18, 1982, https://doi.org/10.1007/bf03323297 DOI: https://doi.org/10.1007/BF03323297

Gordon, William J., Distributive lattices and the approximation of multivariate functions, Approximations with Special Emphasis on Spline Functions (Proc. Sympos. Univ. of Wisconsin, Madison, Wis., 1969), pp. 223-277, Academic Press, New York.

Gordon, William J.; Hall, Charles A. Transfinite element methods: blending-function interpolation over arbitrary curved element domains, Numer. Math., 21, pp. 109-129, 1973/74, https://doi.org/10.1007/bf01436298 DOI: https://doi.org/10.1007/BF01436298

Birou, M., Biermann interpolation with Hermite information, Studia Univ. "Babeş-Bolyai", to appear.

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Published

2005-02-01

How to Cite

Birou, M. (2005). Biermann interpolation of Birkhoff type. Rev. Anal. Numér. Théor. Approx., 34(1), 37–45. https://doi.org/10.33993/jnaat341-789

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