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arXiv · 1905.10593

Optimal subspaces for mean square approximation of classes of differentiable functions with boundary conditions

A. Yu. Ulitskaya·O. L. Vinogradov
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Abstract

In this paper, we specify a set of optimal subspaces for $L_2$ approximation of three classes of functions in the Sobolev space $W^{(r)}_2$, defined on a segment and subject to certain boundary conditions. All of these subspaces are generated by equidistant shifts of a single function. In particular, we indicate optimal spline spaces of all degrees $d\geqslant r-1$ with uniform knots.

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A. Yu. Ulitskaya, O. L. Vinogradov. 2019-05-25. Optimal subspaces for mean square approximation of classes of differentiable functions with boundary conditions. https://arxiv.org/abs/1905.10593

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