On the Best Uniform Polynomial Approximation to the Checkmark Function

Peter D. Dragnev, Alan R. Legg, Ramon Orive

The best uniform polynomial approximation of the checkmark function $f(x)=|x-\alpha |$ is considered, as $\alpha$ varies in $(-1,1)$. For each fixed degree $n$, the minimax error $E_n(\alpha )$ is…