Biermann interpolation of Birkhoff type
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}^...
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| Format: | Article |
| Language: | English |
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Publishing House of the Romanian Academy
2005-02-01
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| Series: | Journal of Numerical Analysis and Approximation Theory |
| Subjects: | |
| Online Access: | https://www.ictp.acad.ro/jnaat/journal/article/view/789 |
| Summary: | 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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| ISSN: | 2457-6794 2501-059X |