An algorithm for Chebyshev approximation by rationals with constrained denominators
type: Item
instance of: scholarly article
title: An algorithm for Chebyshev approximation by rationals with constrained denominators
zbMATH Open document ID: 0886.41013
DOI: 10.1007/BF02433040
author: Martin Gugat
published in: Constructive Approximation
publication date: 1998-05-18T00:00:00Z
review text: Let \(B\) be a compact Hausdorff space, and let \(C(B)\) be the space of all continuous real-valued functions on \(B\). Further it is assumed that: (i) \(\mu\) and \(\nu\) are fixed elements of \(C(B)\) such that \(0<\mu\leq\nu\); (ii) \(Z\) is a nonempty closed subset of \(\mathbb{R}^n\); (iii) \(V\) and \(W\) are continuous maps of \(\mathbb{R}^n\) into \(C(B)\); (iv) \({\mathcal H}\) is a continuous map of \(C(B)\times C(B)\) into \(C(B)\). Based on these data the author proposes a modified differential correction algorithm for determining the value \(\inf_{z\in F} \sup_{t\in B}f(z)(t)\), where \(F:= \{z\in\mathbb{Z}: \mu\leq W(z)\leq\nu\}\) and \(f(z):= {\mathcal H}(V(z),W(z))/ W(z)\). The discussion of this algorithm is completed by convergence results and numerical examples. Finally, it should be mentioned that the algorithm described in the present paper has some advantages in comparison with the original differential correction algorithm.
Mathematics Subject Classification ID: 41A20
Mathematics Subject Classification ID: 65D15
Mathematics Subject Classification ID: 90C32
Mathematics Subject Classification ID: 90C34
zbMATH DE Number: 922394
zbMATH Keywords: algorithm
reviewed by: Wolfgang W. Breckner
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 922394