Geodesic
Splines for three-point rational interpolants with autonomous poles
Daghestan Electronic Mathematical Reports, Tome 7 (2017), pp. 16-28

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For arbitrary grids of nodes $\Delta: a=x_0$ $(N\geqslant 2)$ 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. 
@article{DEMR_2017_7_a1,
     author = {A.-R. K. Ramazanov and V. G. Magomedova},
     title = {Splines for three-point rational interpolants with autonomous poles},
     journal = {Daghestan Electronic Mathematical Reports},
     pages = {16--28},
     publisher = {mathdoc},
     volume = {7},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DEMR_2017_7_a1/}
}
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A.-R. K. Ramazanov; V. G. Magomedova. Splines for three-point rational interpolants with autonomous poles. Daghestan Electronic Mathematical Reports, Tome 7 (2017), pp. 16-28. http://geodesic.mathdoc.fr/item/DEMR_2017_7_a1/