V.T. Shevaldin. Algorithms for the construction of third-order local exponential splines with equidistant knots ... P. 279-287

We construct new local exponential splines with equidistant knots corresponding to a third-order linear differential operator ${\cal L}_3(D)$ of the form
$$
{\cal L}_3(D)=(D-\beta)(D-\gamma)(D-\delta)\quad (\beta,\gamma,\delta\in {\mathbb R}).
$$
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 $W_{\infty}^{{\cal L}_3}$. In particular, for the differential operator ${\cal L}_3(D)=D(D^2-\beta^2)$, 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 ${\cal L}_3(D)$.

Keywords: local exponential splines, linear differential operator, approximation, interpolation

Received June 14, 2019

Revised July19, 2019

Accepted August 5, 2019

Shevaldin Valerii Trifonovich, Dr.Phys.-Math. Sci., Krasovskii Institute of Mathematics and Mechanics Ural Branch of the Russian Academy of Sciences, Yekaterinburg, 620108 Russia, e-mail: Valerii.Shevaldin@imm.uran.ru

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Cite this article as: V.T. Shevaldin. Algorithms for the construction of third-order local exponential splines with equidistant knots, Trudy Instituta Matematiki i Mekhaniki URO RAN, 2019, vol. 25, no. 3, pp. 279–287.