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

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, (≦c ₁ N ^?1 lgN), 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 >c ₀ N ^?1/2. New construction and estimation methods are presented, with possible (e.g., multidimensional) generalizations.