Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2025-01-01T10:26:28.490Z Has data issue: false hasContentIssue false
  • English
  • Français

Non-Convexity in Best Complex Chebyshev Approximation by Rational Functions

Published online by Cambridge University Press:  20 November 2018

Charles B. Dunham
Charles B. Dunham*
Affiliation:
Computer Science Department, University of Western Ontario, London 72, Canada
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In real Chebyshev approximation by generalized rational functions, constraining denominators to be positive guarantees that the set of best coefficients is convex [1, 181]. We show by means of an example that denominators must be constrained to be of constant argument for such a convexity result to hold in complex Chebyshev approximation.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 1 , 01 March 1974 , pp. 115 - 116
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Brosowski, B., Über die Eindeutigkeit der rationalen Tschebysheff-Approximationen, Numer. Math. 7 (1965), 176-186.Google Scholar
2. Dolganov, R. L., The approximation of continuous complex-valued functions by generalized rational functions, Siberian Math. J. 11 (1970), 932-942.Google Scholar