Best local approximation in several variables
type: Item
instance of: scholarly article
title: Best local approximation in several variables
zbMATH Open document ID: 0548.41016
DOI: 10.1016/0021-9045(84)90008-X
author: Harvey Diamond
author: Louise A. Raphael
author: Charles K. Chui
published in: Journal of Approximation Theory
publication date: 1984-01-01T00:00:00Z
review text: The problem of best local approximation in \(R^ n\) is studied. It is proved, in particular, that if V is a \(C^{m+1}\) subspace which is uniquely interpolating at 0 of order m, then the best local approximant from V to any function f which is \(C^{m+1}\) at 0 exists and is uniquely determined by matching all derivatives up through order m with those of f at 0. An analogous result on quasi-rational approximation is also obtained.
Mathematics Subject Classification ID: 41A50
Mathematics Subject Classification ID: 41A63
zbMATH DE Number: 3873930
zbMATH Keywords: best local approximation
zbMATH Keywords: quasi-rational approximation
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3873930