Approximation on \([0,\infty)\) by reciprocals of polynomials with nonnegative coefficients
type: Item
instance of: scholarly article
title: Approximation on \([0,\infty)\) by reciprocals of polynomials with nonnegative coefficients
zbMATH Open document ID: 0532.41029
DOI: 10.1016/0021-9045(84)90133-3
published in: Journal of Approximation Theory
publication date: 1984-01-01T00:00:00Z
review text: This paper considers the problem of best uniform approximation on closed subsets of \([0,\infty)\) of positive continuous functions (decaying to zero at \(\infty)\) by reciprocals of polynomials of degree \(\leq n\) with all coefficients nonnegative. Existence, characterization, (strong) uniqueness, and discretization results are given, along with several examples. It is also shown that if \(n\geq 1\), then approximation on \([0,\infty)\) is equivalent to approximation on [0,b] for some real b; b can be determined constructively. For the corresponding results in the case where only the coefficient of \(x^ n\) is required to be nonnegative, see the authors, Approximation on subsets of \([0,\infty)\) by reciprocals of polynomials, Approximation Theory IV, Academic Press, 553- 559 (1983).
Mathematics Subject Classification ID: 41A50
Mathematics Subject Classification ID: 41A20
Mathematics Subject Classification ID: 41A29
zbMATH DE Number: 3844323
zbMATH Keywords: best uniform approximation
zbMATH Keywords: Existence
zbMATH Keywords: characterization
zbMATH Keywords: uniqueness
zbMATH Keywords: discretization
zbMATH Keywords: reciprocals of polynomials
author: Edwin H. jun. Kaufman
author: D. J. Leeming
author: G. D. (Jerry) Taylor
MaRDI profile type: Publication
full work available at URL: 0021-9045(84)90133-3
OpenAlex ID: W2072853426
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description: scientific article; zbMATH DE number 3844323