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

Vladislav Babenko, Yuliya Babenko, Nataliya Parfinovich, Dmytro Skorokhodov

• In this paper we study the best asymmetric (sometimes also called penalized or sign-sensitive) approximation in the metrics of the space Lp, 1≤p ≥∞, of functions f ∈ C² (0, 1)² with nonnegative Hessian by piecewise linear splines s ∈ S(△N ), generated by given triangulations △N with N elements. We find the exact asymptotic behavior of the optimal (over triangulations △N and splines s ∈ S(△N )) error of such an approximation as N → ∞