Some Nonlinear Operators Are as Easy to Approximate as the Identity Operator

Wasilkowski, Grzegorz W.

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


More About This Work

Academic Units
Computer Science
Department of Computer Science, Columbia University
Columbia University Computer Science Technical Reports, CUCS-058-83
Published Here
October 25, 2011