Barycentric formulae for some optimal rational approximants involving Blaschke products
type: Item
instance of: scholarly article
title: Barycentric formulae for some optimal rational approximants involving Blaschke products
zbMATH Open document ID: 0708.65013
DOI: 10.1007/BF02247966
published in: Computing
publication date: 1990-01-01T00:00:00Z
review text: If the value Lf of some bounded linear functional L for \(f\in H^ 2(D)\) is to be approximated, optimal formulas often refer to rational approximation. The evaluation of the interpolant can be performed by O(n) operations if a precalculation (with \(0(n^ 2)\) operations) has been done. On the other hand, some formulas for this process may be sensitive to rounding errors. This sensitivity is reduced by refering to barycentric coordinates. Moreover the connection between some formulas of \textit{F. Stenger} [Math. Comput. 47, 225-252 (1986; Zbl 0592.41019)] and of \textit{F. M. Larkin} [Approx., Theory and Appl. Proc. Int. Symp. Tampa/Florida 1976, 257-288 (1977; Zbl 0368.41032)] are elucidated.
reviewed by: D. Braess
Mathematics Subject Classification ID: 65D15
Mathematics Subject Classification ID: 41A20
zbMATH DE Number: 4164003
zbMATH Keywords: Blaschke products
zbMATH Keywords: bounded linear functional
zbMATH Keywords: optimal formulas
zbMATH Keywords: rational approximation
zbMATH Keywords: rounding errors
zbMATH Keywords: sensitivity
zbMATH Keywords: barycentric coordinates
author: Jean-Paul Berrut
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02247966
OpenAlex ID: W8231882
description: scientific article; zbMATH DE number 4164003