1984 Reports

Some Nonlinear Problems Are as Easy as the Approximation Problem

Wasilkowski, Grzegorz W.

In this paper we study the following problem. Given an operator S and a subset F0 of some linear space, approximate S (f) for any f ∈ F0 possessing only partial information on f. Although all operators S considered here are nonlinear (e.g. min f(x). min|f(x) |. 1/f or ||f||, we prove that these problems are "equivalent" to the problem of approximating S(j)=f. i.e. S=I. This equivalence provides optimal (or nearly optimal) information and algorithms.