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arXiv · 1311.7408

Exact asymptotics of the optimal Lp-error of asymmetric linear spline approximation

Vladyslav Babenko·Yuliya Babenko·Nataliya Parfinovych·Dmytro Skorokhodov
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Abstract

In this paper we study the best asymmetric (sometimes also called penalized or sign-sensitive) approximation in the metrics of the space $L_p$, $1\leqslant p\leqslant\infty$, of functions $f\in C^2\left([0,1]^2\right)$ with nonnegative Hessian by piecewise linear splines $s\in S(\triangle_N)$, generated by given triangulations $\triangle_N$ with $N$ elements. We find the exact asymptotic behavior of optimal (over triangulations $\triangle_N$ and splines $s\in S(\triangle_N)$ error of such approximation as $N\to \infty$.

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Vladyslav Babenko, Yuliya Babenko, Nataliya Parfinovych, Dmytro Skorokhodov. 2013-11-28. Exact asymptotics of the optimal Lp-error of asymmetric linear spline approximation. https://arxiv.org/abs/1311.7408

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