INTERPOLATION WITH MINIMUM VALUE OF \(L_{2}\)-NORM OF DIFFERENTIAL OPERATOR
For the class of bounded in \(l_{2}\)-norm interpolated data, we consider a problem of interpolation on a finite interval \([a,b]\subset\mathbb{R}\) with minimal value of the \(L_{2}\)-norm of a differential operator applied to interpolants. Interpolation is performed at knots of an arbitrary \(N\)...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
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Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and Mechanics
2024-12-01
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| Series: | Ural Mathematical Journal |
| Subjects: | |
| Online Access: | https://umjuran.ru/index.php/umj/article/view/840 |
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| Summary: | For the class of bounded in \(l_{2}\)-norm interpolated data, we consider a problem of interpolation on a finite interval \([a,b]\subset\mathbb{R}\) with minimal value of the \(L_{2}\)-norm of a differential operator applied to interpolants. Interpolation is performed at knots of an arbitrary \(N\)-point mesh \(\Delta_{N}:\ a\leq x_{1}<x_{2}<\cdots <x_{N}\leq b\). The extremal function is the interpolating natural \({\cal L}\)-spline for an arbitrary fixed set of interpolated data. For some differential operators with constant real coefficients, it is proved that on the class of bounded in \(l_{2}\)-norm interpolated data, the minimal value of the \(L_{2}\)-norm of the differential operator on the interpolants is represented through the largest eigenvalue of the matrix of a certain quadratic form. |
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| ISSN: | 2414-3952 |