Geodesic
A Method for the Construction of Local Parabolic Splines with Additional Knots
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 25 (2019) no. 2, pp. 205-219

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We propose a general method for the construction of local parabolic splines with an arbitrary arrangement of knots for functions given on grid subsets of the number axis or its segment. Special cases of this scheme are Yu. N. Subbotin's and B. I. Kvasov's splines. For Kvasov's splines, we consider boundary conditions different from those suggested by Kvasov. We study the approximating and smoothing properties of these splines in the case of uniform knots. In particular, we find two-sided estimates for the error of approximation of the function classes $W_{\infty}^2$ and $W_{\infty}^3$ by these splines in the uniform metric and calculate the exact uniform Lebesgue constants and the norms of the second derivatives on the class $W_{\infty}^2$. These properties are compared with the corresponding properties of Subbotin's splines.
Keywords: local parabolic splines, approximation, equally spaced knots.
Mots-clés : interpolation 
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     author = {Yu. N. Subbotin and V. T. Shevaldin},
     title = {A {Method} for the {Construction} of {Local} {Parabolic} {Splines} with {Additional} {Knots}},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {205--219},
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     number = {2},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2019_25_2_a19/}
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Yu. N. Subbotin; V. T. Shevaldin. A Method for the Construction of Local Parabolic Splines with Additional Knots. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 25 (2019) no. 2, pp. 205-219. http://geodesic.mathdoc.fr/item/TIMM_2019_25_2_a19/