Advertisement

Springer Nature is making Coronavirus research free. View research | View latest news | Sign up for updates

Failure of Loeb's method for rational L1 approximation

Versagen der Loebschen Methode für rationelle L1-Annäherungen

  • 26 Accesses

Abstract

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.

Zusammenfassung

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.

This is a preview of subscription content, log in to check access.

References

  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).

  2. [2]

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

  3. [3]

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

Download references

Author information

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Dunham, C.B. Failure of Loeb's method for rational L1 approximation. Computing 13, 235–237 (1974). https://doi.org/10.1007/BF02241716

Download citation

Keywords

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