Sharpened polynomial approximation
A.G. Law, Ann L. McKerracher · Pacific Journal of Mathematics · 1974
In 1951, W. Wolibner showed that a real continuous function on a closed interval can be uniformly approximated by a polynomial which interpolates at prescribed points and which has a uniform norm agreeing with the function's.This fit can be sharpened to include matching of some relative extrema as well.The paper characterizes functions that permit Simultaneous Approximation and Interpolation which is Norm-Preserving and Extrema-Matching over the entire interval except, perhaps, for a subset of arbitrarily-small diameter.