Some nonlinear problems are as easy as the approximation problem

G. W. Wasilkowski

doi:10.1016/0898-1221(84)90063-4

Some nonlinear problems are as easy as the approximation problem

G. W. Wasilkowski

Computer Science

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

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 language	English
Pages (from-to)	351-363
Number of pages	13
Journal	Computers and Mathematics with Applications
Volume	10
Issue number	4-5
DOIs	https://doi.org/10.1016/0898-1221(84)90063-4
State	Published - 1984

Bibliographical note

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

Funding

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

Funders	Funder number
National Science Foundation (NSF)	DCR 82-14322

ASJC Scopus subject areas

Modeling and Simulation
Computational Theory and Mathematics
Computational Mathematics

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10.1016/0898-1221(84)90063-4

Cite this

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abstract = "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.",

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AU - Wasilkowski, G. W.

N1 - Funding Information: *This research was supported in part by the National Science Foundation under Grant DCR 82-14322.

PY - 1984

Y1 - 1984

N2 - 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.

AB - 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.

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EP - 363

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

IS - 4-5

ER -

Some nonlinear problems are as easy as the approximation problem

Abstract

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