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This article is cited in 1 scientific paper (total in 1 paper)
Extremal functional $L_p$-interpolation on an arbitrary mesh on the real axis
Yu. N. Subbotin, V. T. Shevaldin N. N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences, Ekaterinburg, Russia
Abstract:
The Golomb-de Boor problem of extremal interpolation of infinite real sequences with smallest $L_p$-norm of the $n$th derivative of the interpolant, $1\le p\le \infty$, on an arbitrary mesh on the real axis is studied under constraints on the norms of the corresponding divided differences. For this smallest norm, lower estimates are obtained for any $n\in \mathbb N$ in terms of $B$-splines. For the second derivative, this quantity is estimated from below and above by constants depending on the parameter $p$.
Bibliography: 13 titles.
Keywords:
extremal interpolation, derivative, divided difference, spline, difference equation.
Received: 19.06.2021
Citation:
Yu. N. Subbotin, V. T. Shevaldin, “Extremal functional $L_p$-interpolation on an arbitrary mesh on the real axis”, Mat. Sb., 213:4 (2022), 123–144; Sb. Math., 213:4 (2022), 556–577
Linking options:
https://www.mathnet.ru/eng/sm9628https://doi.org/10.1070/SM9628 https://www.mathnet.ru/eng/sm/v213/i4/p123
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Abstract page: | 277 | Russian version PDF: | 33 | English version PDF: | 25 | Russian version HTML: | 73 | References: | 36 | First page: | 24 |
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