Geodesic
Algorithms for the construction of third-order local exponential splines with equidistant knots
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 25 (2019) no. 3, pp. 279-287

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We construct new local exponential splines with equidistant knots corresponding to a third-order linear differential operator $\mathcal L_3(D)$ of the form $$ \mathcal L_3(D)=(D-\beta)(D-\gamma)(D-\delta)\quad (\beta,\gamma,\delta\in \mathbb R). $$ We also establish upper order estimates for the error of approximation by these splines in the uniform metric on the Sobolev class of three times differentiable functions $W_{\infty}^{\mathcal L_3}$. In particular, for the differential operator $\mathcal L_3(D)=D(D^2-\beta^2)$, we give a general scheme for the construction of local splines with additional knots, which leads in one case to known shape-preserving splines and in another case to new local interpolation splines exact on the kernel of $\mathcal L_3(D)$.
Keywords: local exponential splines, linear differential operator, approximation
Mots-clés : interpolation. 
@article{TIMM_2019_25_3_a22,
     author = {V. T. Shevaldin},
     title = {Algorithms for the construction of third-order local exponential splines with equidistant knots},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {279--287},
     publisher = {mathdoc},
     volume = {25},
     number = {3},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2019_25_3_a22/}
}
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V. T. Shevaldin. Algorithms for the construction of third-order local exponential splines with equidistant knots. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 25 (2019) no. 3, pp. 279-287. http://geodesic.mathdoc.fr/item/TIMM_2019_25_3_a22/