Geodesic
Approximation by local $\mathcal L$-splines that are exact on subspaces of the kernel of a differential operator
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 4, pp. 272-280
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We construct local $\mathcal L$-splines with uniform nodes that preserve subsets from the kernel of a linear differential operator $\mathcal L$ of order $r$ with constant real coefficients and pairwise distinct roots of the characteristic polynomial. Pointwise estimates are found for the error of approximation by the constructed $\mathcal L$-splines on classes of functions defined by differential operators of orders smaller than $r$.
Keywords: approximation, local $\mathcal L$-splines, differential operator. 
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E. V. Strelkova; V. T. Shevaldin. Approximation by local $\mathcal L$-splines that are exact on subspaces of the kernel of a differential operator. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 4, pp. 272-280. http://geodesic.mathdoc.fr/item/TIMM_2010_16_4_a25/

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