Geodesic
Approximations by polynomial and trigonometric splines of third order preserving some properties of approximated functions
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 13 (2007) no. 2, pp. 156-166

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In this paper with the help of parabolic splines we construct a linear method of approximate recovery of functions by their values on an arbitrary grid. In the method, a spline inherits the properties of monotonicity and convexity from the approximated function, and is sufficiently smooth. In addition, the constructed linear operator as an operator acting from the space of continuous functions to the same space has the norm equal to one. We also obtain similar results for trigonometric splines of third order. 
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     title = {Approximations by polynomial and trigonometric splines of third order preserving some properties of approximated functions},
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Yu. N. Subbotin. Approximations by polynomial and trigonometric splines of third order preserving some properties of approximated functions. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 13 (2007) no. 2, pp. 156-166. http://geodesic.mathdoc.fr/item/TIMM_2007_13_2_a14/