Rational Carathéodory-Fejér approximation on a disk, a circle, and an interval
type: Item
instance of: scholarly article
title: Rational Carathéodory-Fejér approximation on a disk, a circle, and an interval
zbMATH Open document ID: 0543.41016
DOI: 10.1016/0021-9045(84)90101-1
author: Martin H. Gutknecht
published in: Journal of Approximation Theory
publication date: 1984-01-01T00:00:00Z
review text: A systematic description of the Carathéodory-Fejér method (CF method) is given for near-best uniform rational approximation of a (high degree) polynomial on a disk. On the basis of Takagi's extension of the Carathéodory-Fejér theorem degeneracies are characterized and it is proven that they appear in the CF table, which is introduced, in square blocks. Corresponding methods for complex and real trigonometric rational approximation, and for ordinary real rational approximation on an interval are then derived. For each problem certain weight functions are allowed and several types of CF approximation are defined depending on truncation. In Part II of ''On complex rational approximation'' [in ''Computational Aspects of Complex Analysis'', H. Werner et al., eds., D. Reidel Publ. Co., Dordrecht (1983), pp. 103-132] these results have meanwhile been extended to the case where the given function is a higher degree rational function.
Mathematics Subject Classification ID: 41A20
Mathematics Subject Classification ID: 41A10
Mathematics Subject Classification ID: 65D15
Mathematics Subject Classification ID: 30E10
zbMATH DE Number: 3863787
zbMATH Keywords: Carathéodory-Fejér method
zbMATH Keywords: CF method
zbMATH Keywords: near-best uniform rational approximation
zbMATH Keywords: Takagi's extension
zbMATH Keywords: weight functions
MaRDI profile type: Publication
full work available at URL: 0021-9045(84)90101-1
OpenAlex ID: W2022323026
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description: scientific article; zbMATH DE number 3863787