How powerful is continuous nonlinear information for linear problems?
type: Item
instance of: scholarly article
title: How powerful is continuous nonlinear information for linear problems?
zbMATH Open document ID: 0618.65043
DOI: 10.1016/0885-064X(86)90008-7
published in: Journal of Complexity
publication date: 1986-01-01T00:00:00Z
review text: The paper discusses the question, how much information one can deduce about the best approximation of a solution to a problem which depends on an unknown function f, of which only partial information N(f) is known; here N is an operator defined on a given class of functions with values in \({\mathbb{R}}^ n\); cf. the book by \textit{J. F. Traub}, the second author and \textit{H. Wózniakowski} [Information, uncertainty, complexity. (1983; Zbl 0522.68041)]. While many results are known for linear information operators, this paper discusses the nonlinear, but continuous, case. It is shown that for worst case behaviour, nonlinear information gives no less uncertainty than suitable linear information, while on the average, the uncertainty can be considerably reduced.
Mathematics Subject Classification ID: 65J05
Mathematics Subject Classification ID: 41A46
zbMATH DE Number: 4003378
zbMATH Keywords: information operator
zbMATH Keywords: best approximation
zbMATH Keywords: partial information
zbMATH Keywords: worst case behaviour
zbMATH Keywords: nonlinear information
author: Bolesław Kacewicz
author: Grzegorz W. Wasilkowski
MaRDI profile type: Publication
cites work: Q5336643
cites work: Optimality of Euler-integral information for solving a scalar autonomous ODE
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cites work: Average case optimality for linear problems
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cites work: Average case optimal algorithms in Hilbert spaces
description: scientific article; zbMATH DE number 4003378