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Failure of Loeb's method for rational L1 approximation

Versagen der Loebschen Methode für rationelle L1-Annäherungen

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An algorithm for rational L1 approximation on an interval is obtained by adapting Loeb's weighted minimax algorithm for rational Chebyshev approximation on an interval. Sufficient conditions for the algorithm to fail are given.


Entwickelt wird ein Algorithmus für rationelle L1-Annäherungen an einem Intervall durch Anpassung des Loebschen gewogenen Minimax-Algorithmus für rationale Chebyshev-Annäherungen an einem Intervall. Hinreichende Bedingungen für das Versagen des Algorithmus werden gegeben.

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  1. [1]

    Barrodale, I., Mason, J. C.: Two simple algorithms for discrete rational approximation, Technical Report No. 15, Computer Science Department, University of Toronto. Also appeared as Report No. 29, Departments of Mathematics, University of Victoria and in Math. Comp.24, 877–891 (1970).

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    Cheney, E. W., Goldstein, A. A.: Mean-square approximation by generalized rational functions. Math. Zeitschr.95, 232–241 (1967).

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    Dunham, C. B.: Degeneracy in mean rational approximation. J. Approx. Theory4, 235–239 (1971).

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Dunham, C.B. Failure of Loeb's method for rational L1 approximation. Computing 13, 235–237 (1974).

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  • Computational Mathematic
  • Chebyshev Approximation
  • Minimax Algorithm
  • Rational Chebyshev Approximation
  • Weighted Minimax