An optimal sequential algorithm for the uniform approximation of convex functions on $[0,1]^2$.

TL;DRAbstract

In this paper an algorithm is given for the sequential selection ofN nodes (i.e., measurement points) for the uniform approximation (recovery) of convex functions over [0, 1]2, which has almost optimal order global error, (źc1Nź1lgN), over a naturally defined class of convex functions. This shows the essential superiority of sequential algorithms for this class of approximation problems because any simultaneous choice ofN nodes leads to a global error >c0Nź1/2. New construction and estimation methods are presented, with possible (e.g., multidimensional) generalizations.

Chat with Paper

AI Agents for this Paper