The Polynomial Carathéodory—Fejér Approximation Method for Jordan Regions

We propose a method for the approximation of analytic functions on Jordan regions that is based on a Carathéodory—Fejér type of economization of the Faber series. The method turns out to be very effective if the boundary of the region is analytic. It often still works when the region degenerates to...

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Bibliographic Details
Published in:IMA journal of numerical analysis 1983-04, Vol.3 (2), p.207-220
Main Authors: ELLACOTT, S. W., GUTKNECHT, M. H.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical approximation
Sciences and techniques of general use
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Summary:We propose a method for the approximation of analytic functions on Jordan regions that is based on a Carathéodory—Fejér type of economization of the Faber series. The method turns out to be very effective if the boundary of the region is analytic. It often still works when the region degenerates to a Jordan arc. We also derive related lower and upper bounds for the error of the best approximation.
ISSN:0272-4979
1464-3642
DOI:10.1093/imanum/3.2.207