Some nonlinear problems are as easy as the approximation problem

G. W. Wasilkowski

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


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 fε{lunate}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(f) = f, i.e. S = I. This equivalence provides optimal (or nearly optimal) information and algorithms.

Original languageEnglish
Pages (from-to)351-363
Number of pages13
JournalComputers and Mathematics with Applications
Issue number4-5
StatePublished - 1984

Bibliographical note

Funding Information:
*This research was supported in part by the National Science Foundation under Grant DCR 82-14322.

ASJC Scopus subject areas

  • Modeling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics


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