On linearity of spline algorithms
type: Item
instance of: scholarly article
title: On linearity of spline algorithms
zbMATH Open document ID: 0681.65005
DOI: 10.1016/0885-064X(89)90007-1
author: Mark Kon
author: Roberto Tempo
published in: Journal of Complexity
publication date: 1989-01-01T00:00:00Z
review text: The main result of this paper can be stated in a simple form as follows: Let F and Z be Banach spaces. Then, if the dimension of F is greater than 2, statements (a) through (e) are equivalent: (a) F is a Hilbert space. For every linear problem S with domain F and information operator N there exists (b) a linear spline algorithm. (c) a linear interpolatory algorithm, (d) a linear strongly optimal algorithm, (e) a linear almost strongly optimal algorithm. In the context of information-based complexity, this provides a converse to the well-known result that a Hilbert structure is sufficient for such linearity properties.
Mathematics Subject Classification ID: 65D07
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 65D05
Mathematics Subject Classification ID: 41A05
zbMATH DE Number: 4115815
zbMATH Keywords: optimal recovery
zbMATH Keywords: Banach spaces
zbMATH Keywords: Hilbert space
zbMATH Keywords: linear spline algorithm
zbMATH Keywords: linear interpolatory algorithm
zbMATH Keywords: linear strongly optimal algorithm
zbMATH Keywords: linear almost strongly optimal algorithm
zbMATH Keywords: information-based complexity
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4115815