Geodesic
Orders of approximation by local exponential splines
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 4, pp. 135-144

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We continue the study of approximation properties of local exponential splines on a uniform grid with step $h>0$ corresponding to a linear differential operator $\mathcal L$ with constant coefficients and real pairwise different roots of the characteristic polynomial (such splines were constructed by E. V. Strelkova and V. T. Shevaldin). We find order estimates as $h\to0$ for the error of approximation of certain Sobolev classes of functions by the mentioned splines, which are exact on the kernel of the operator $\mathcal L$.
Keywords: approximation, local exponential splines, order estimates. 
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     title = {Orders of approximation by local exponential splines},
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Yu. S. Volkov; E. G. Pytkeev; V. T. Shevaldin. Orders of approximation by local exponential splines. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 4, pp. 135-144. http://geodesic.mathdoc.fr/item/TIMM_2012_18_4_a11/