It is shown that a function inL 1 has a best approximation by convex functions, and that the net of bestL p approximations converges asp decreases to one.

1. H.G Burchard. Extremal positive splines with applications to interpolation and approximation by Generalized convex functions · 2. H.G Burchard. Interpolation ...

It is shown that a function inL1 has a best approximation by convex functions, and that the net of bestLp approximations converges asp decreases to one.

We give elementary proofs for the existence and uniqueness of the best L1-approximation to a continuous function from the class of convex functions on a ...

approximation by Generalized convex functions, Bull. Amer. Math. Sot. 79 (1973),. 959-964. 2. H. G. BURCHARD, “Interpolation and Approximation by Generalized ...

Best L1-approximation by generalized convex functions · Contents. Journal of Approximation Theory. Volume 59, Issue 1 · PREVIOUS ARTICLE. Generalized ...

Jun 14, 2024 · types of convex functions Φ and for some finite dimensional approximation classes of func- ... Micchelli, C. A. (1977) Best L1 approximation ...

We consider here best approximation by n-convex functions. We first show that if f∈L1[0,1], then there is, a best L1-approximant to f by functions wh.

Zwick, Existence of best n-convex approximations, Proc. Amer. Math. Soc. 97 (1986),. 273-276. 26. -, Best L1 -approximation by generalized convex functions, J.

Mar 23, 2020 · Piecewise affine approximation of a convex function · For all x∈R holds f(x)≥fN(x). · Reformulate (PN) as a LP in canonical form mincTx s.t. Ax= ...