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This article is cited in 6 scientific papers (total in 6 papers)
Splines for three-point rational interpolants with autonomous poles
A.-R. K. Ramazanovab, V. G. Magomedovaa a Daghestan State University, Makhachkala
b Daghestan Scientific Centre of Russian Academy of Sciences, Makhachkala
Abstract:
For arbitrary grids of nodes $\Delta: a=x_0<x_1<\dots<x_N=b$ $(N\geqslant 2)$ smooth
splines for three–point rational interpolants are constructed,
the poles of interpolants depend on nodes and the free parameter $\lambda$.
Sequences of such splines and their derivatives for all functions $f(x)$
respectively of the classes of $C_{[a,b]}^{(i)}$ $(i=0,1,2)$ under the condition
$\|\Delta\| \to 0$ uniformly in $[a,b]$ converge respectively to $f^{(i)}(x)$ $(i=0,1,2)$
(depending on the parameter $\lambda$).
Bonds for the convergence rate are found in terms of the distance between the
nodes.
Keywords:
splines, interpolation splines, rational splines.
Received: 11.03.2017 Revised: 24.03.2017 Accepted: 27.03.2017
Citation:
A.-R. K. Ramazanov, V. G. Magomedova, “Splines for three-point rational interpolants with autonomous poles”, Daghestan Electronic Mathematical Reports, 2017, no. 7, 16–28
Linking options:
https://www.mathnet.ru/eng/demr33 https://www.mathnet.ru/eng/demr/y2017/i7/p16
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Abstract page: | 127 | Full-text PDF : | 38 | References: | 15 |
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