On the best non-symmetric $$$L_1$$$-approximations under the constraints on their derivatives

Ye.V. D'yakova; I.A. Shevchenko

doi:10.15421/241505

On the best non-symmetric $$$L_1$$$-approximations under the constraints on their derivatives

Ye.V. D'yakova (Oles Honchar Dnipropetrovsk National University)
I.A. Shevchenko (Oles Honchar Dnipropetrovsk National University)

Abstract

We obtained exact values of the best $$$L_1$$$-approximations of classes $$$W^r_1$$$ and $$$W^{r-1}_V$$$, non-symmetric and one-way $$$L_1$$$-approximation of classes $$$W^r_1$$$ of periodic functions by splines of order $$$r$$$ and $$$r-1$$$ with defect 1 and knots at the points $$$t_j = \frac{2\pi}{n} \left[\frac{j}{2}\right] + (1 - (-1)^j) \frac{h}{2}$$$, $$$j\in \mathbb{Z}$$$ that belong to the class $$$W^r_1$$$ and $$$W^{r-1}_V$$$.

Keywords

spline; the best non-symmetric approximation; the best one-way approximation; Sobolev classes

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References

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