Geodesic
Local approximation by splines with displacement of nodes
Matematičeskie trudy, Tome 14 (2011) no. 2, pp. 73-82

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We consider the problem of approximating a function defined on a uniform mesh by the method of local polynomial spline-approximation where the mesh of the nodes of the spline is chosen displaced relative to the mesh of the initial data. Conditions are established for the local form preservation by the spline of the initial data. We study the approximative properties of the method for the case of the simplest local approximation formula and find the optimal values of the displacement parameters. 
@article{MT_2011_14_2_a3,
     author = {Yu. S. Volkov and E. V. Strelkova and V. T. Shevaldin},
     title = {Local approximation by splines with displacement of nodes},
     journal = {Matemati\v{c}eskie trudy},
     pages = {73--82},
     publisher = {mathdoc},
     volume = {14},
     number = {2},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2011_14_2_a3/}
}
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Yu. S. Volkov; E. V. Strelkova; V. T. Shevaldin. Local approximation by splines with displacement of nodes. Matematičeskie trudy, Tome 14 (2011) no. 2, pp. 73-82. http://geodesic.mathdoc.fr/item/MT_2011_14_2_a3/