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: 173

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

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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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