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Matematicheskie Zametki, 1968, Volume 4, Issue 2, Pages 233–238
(Mi mzm6765)
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This article is cited in 39 scientific papers (total in 39 papers)
Kolmogorov-type inequalities and the best formulas for numerical differentiation
L. V. Taikov V. A. Steklov Institute of Mathematics, Sverdlovsk Branch of the Academy of Sciences of USSR
Abstract:
For a certain class of complex-valued functions $f(x)$, $-\infty<x<\infty$, is found the best approximation
$$
u_N=\inf_{\|A\|\le N}\sup_{\|f^{(n)}\|_{L_2}\le1}\|f^{(k)}-A(f)\|C
$$
of a differential operator by linear operators $A$ with the norm $\|A\|_{L_2}^C\le N$, $N>0$. Using the value $u_N$, the smallest constant $Q$ in the inequality
$$
\|f^{(k)}\|_Q\le Q\|f\|_{L_2}^\alpha\|f^{(n)}\|^\beta_{L_2}
$$
is found.
Received: 19.12.1967
Citation:
L. V. Taikov, “Kolmogorov-type inequalities and the best formulas for numerical differentiation”, Mat. Zametki, 4:2 (1968), 233–238; Math. Notes, 4:2 (1968), 631–634
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https://www.mathnet.ru/eng/mzm6765 https://www.mathnet.ru/eng/mzm/v4/i2/p233
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Abstract page: | 675 | Full-text PDF : | 269 | First page: | 2 |
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