On the adaptive and continuous information problems
type: Item
instance of: scholarly article
title: On the adaptive and continuous information problems
zbMATH Open document ID: 0688.65036
DOI: 10.1016/0885-064X(89)90030-7
author: Mark Kon
author: Erich Novak
published in: Journal of Complexity
publication date: 1989-01-01T00:00:00Z
review text: The paper deals with the adaption issue, showing that it can help for linear problems. For such problems (in a Banach space setting), the infimum of the ratio of adaptive and nonadaptive information is determined and related results are derived: let a and b respectively denote this infimum and the same infimum over all linear problems with Hilbert space range; then \(1/2\leq a\leq \sqrt{.8665}\) and \(\sqrt{2}/2<b<\sqrt{.8665}.\) Similar results are derived for finite- dimensional and \(L^ p\) range spaces. It is also shown that continuous information yields a smaller radius of information (error) than linear information in a Banach space.
reviewed by: N.A.Warsi
Mathematics Subject Classification ID: 65J10
Mathematics Subject Classification ID: 47A50
zbMATH DE Number: 4128308
zbMATH Keywords: adaptive information
zbMATH Keywords: Banach space
zbMATH Keywords: nonadaptive information
zbMATH Keywords: Hilbert space
zbMATH Keywords: radius of information
MaRDI profile type: Publication
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full work available at URL: 0885-064x(89)90030-7
OpenAlex ID: W1980039889
description: scientific article; zbMATH DE number 4128308