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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
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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