Best \(L_ 1\)-approximation
type: Item
instance of: scholarly article
title: Best \(L_ 1\)-approximation
zbMATH Open document ID: 0543.41029
DOI: 10.1016/0021-9045(84)90087-X
published in: Journal of Approximation Theory
publication date: 1984-01-01T00:00:00Z
review text: This paper studies best \(L_ 1\)-approximation of continuous functions defined on an interval [a,b]. First a condition is established ensuring uniqueness of best \(L_ 1\)-approximation. This condition can be considered as a generalized Haar condition. Using it, a short proof of uniqueness of best \(L_ 1\)-approximation from subspaces of spline functions is given. Then the relationship between best \(L_ 1\)- approximation and certain classes of perfect splines is considered. These results can be applied to construct bounds for the error of best \(L_ 1\)-approximations from spline subspaces. These estimates have an application in numerical integration.
Mathematics Subject Classification ID: 41A52
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 41A50
zbMATH DE Number: 3863800
zbMATH Keywords: perfect splines
zbMATH Keywords: bounds
zbMATH Keywords: error
zbMATH Keywords: best \(L_ 1\)-approximations
zbMATH Keywords: numerical integration
author: Hans Strauss
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3863800