Optimal approximation order of piecewise constants on convex partitions

Oleg Davydov, Oleksandr Kozynenko, Dmytro Skorokhodov

We prove that the error of the best nonlinear $L_p$-approximation by piecewise constants on convex partitions is $\mathcal{O}\left(N^{-\frac{2}{d+1}}\right)$, where $N$ the number of…