Abstract:
In this paper, the local $\mathcal L$-splines of odd order with uniform nodes are constructed. These splines preserve basic functions from the kernel of the linear differential operator $\mathcal L$ with constant real coefficients and pairwise different roots of a characteristic polynomial. The pointwise error estimation of an approximation value using constructed splines on appropriate classes of differentiable functions is given.
Key words:local $\mathcal L$-splines, differential operator, the error of an approximation.
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