Geodesic
Approximation by third-order local $\mathcal L$-splines with uniform nodes
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 4, pp. 156-165

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For a third-order linear differential operator of the form $\mathcal L_3=(D-\beta)(D-\gamma)(D-\delta)$ ($D$ is the differentiation symbol and $\beta,\gamma$, and $\delta$ are pairwise distinct real numbers) on the class of functions $W_\infty^{\mathcal L_2}$, where $\mathcal L_2=(D-\beta)(D-\gamma)$, a sharp pointwise estimate is found for the error of approximation by local noninterpolational $\mathcal L$- spines with uniform nodes corresponding to the operator $\mathcal L_3$; these splines were constructed by the authors earlier.
Keywords: approximation, local $\mathcal L$-splines
Mots-clés : uniform nodes. 
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     title = {Approximation by third-order local $\mathcal L$-splines with uniform nodes},
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     language = {ru},
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P. G. Zhdanov; V. T. Shevaldin. Approximation by third-order local $\mathcal L$-splines with uniform nodes. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 4, pp. 156-165. http://geodesic.mathdoc.fr/item/TIMM_2010_16_4_a14/