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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.

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Academic Units
Computer Science
Publisher
Department of Computer Science, Columbia University
Series
Columbia University Computer Science Technical Reports, CUCS-148-84
Published Here
February 23, 2012
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