The optimal dyadic derivative

The optimal dyadic derivative

We show that the best approximation to the difference operators on the cyclic groups of order 2 n by a dyadic convolution operator are the restrictions of a generalized dyadic derivative. This answers a question on the “intuitive” interpretation of the dyadic derivative posed by Butzer and Wagner mo...

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Veröffentlicht in:Analysis mathematica (Budapest) 2014-12, Vol.40 (4), p.287-299
1. Verfasser: Klotz, Andreas
Format: Artikel
Sprache:eng
Schlagworte:
Analysis
Approximation
Constrictions
Convolution
Derivatives
Dyadics
Mathematical analysis
Mathematics
Mathematics and Statistics
Operators
Optimization
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Zusammenfassung:We show that the best approximation to the difference operators on the cyclic groups of order 2 n by a dyadic convolution operator are the restrictions of a generalized dyadic derivative. This answers a question on the “intuitive” interpretation of the dyadic derivative posed by Butzer and Wagner more than 30 years ago.
ISSN:0133-3852
1588-273X
DOI:10.1007/s10476-014-0403-4