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

Producción científica: Article › revisión exhaustiva

15 Citas (Scopus)

Resumen

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.

Idioma original	English
Páginas (desde-hasta)	351-363
Número de páginas	13
Publicación	Computers and Mathematics with Applications
Volumen	10
N.º	4-5
DOI	https://doi.org/10.1016/0898-1221(84)90063-4
Estado	Published - 1984

Nota bibliográfica

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

Financiación

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

Financiadores	Número del financiador
National Science Foundation Arctic Social Science Program	DCR 82-14322

ASJC Scopus subject areas

Modeling and Simulation
Computational Theory and Mathematics
Computational Mathematics

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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.",

author = "Wasilkowski, \{G. W.\}",

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

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language = "English",

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T1 - Some nonlinear problems are as easy as the approximation problem

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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UR - https://www.scopus.com/pages/publications/0021585258#tab=citedBy

U2 - 10.1016/0898-1221(84)90063-4

DO - 10.1016/0898-1221(84)90063-4

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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

Resumen

Nota bibliográfica

Financiación

ASJC Scopus subject areas

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