Geodesic
Splines on rational interpolants
Daghestan Electronic Mathematical Reports, Tome 4 (2015), pp. 21-30

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For a function continuous on a given interval (or periodic) we construct $n$-point ($n=2,3,4$) rational interpolants and rational splines by means of of these interpolants. The sequences of the splines by the n-point interpolants for $n = 2$ and $n=3$ converges uniformly on the entire interval to the function itself for any sequence of grids with a diameter tending to zero. For $n= 3$ this property of unconditional convergence is also transmitted to the first derivatives, and for $n = 4$ – to the first and second derivatives. We also give estimates of the convergence rate.
Keywords: splines, interpolation rational splines, unconditional convergence. 
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     author = {A.-R. K. Ramazanov and V. G. Magomedova},
     title = {Splines on rational interpolants},
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A.-R. K. Ramazanov; V. G. Magomedova. Splines on rational interpolants. Daghestan Electronic Mathematical Reports, Tome 4 (2015), pp. 21-30. http://geodesic.mathdoc.fr/item/DEMR_2015_4_a2/