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The Newton differential correction algorithm for rational Chebyshev approximation with constrained denominators

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Abstract

An algorithm for constrained rational Chebyshev approximation is introduced that combines the idea of an algorithm due to Hettich and Zencke, for which superlinear convergence is guaranteed, with the auxiliary problem used in the well-known original differential correction method. Superlinear convergence of the algorithm is proved. Numerical examples illustrate the fast convergence of the method and its advantages compared with the algorithm of Hettich and Zencke.

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Communicated by M. H. Gutknecht

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Gugat, M. The Newton differential correction algorithm for rational Chebyshev approximation with constrained denominators. Numer Algor 13, 107–122 (1996). https://doi.org/10.1007/BF02143129

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Keywords

  • Rational Chebyshev approximation with constrained denominators
  • parametric auxiliary problem
  • parametric optimization
  • Newton's method
  • superlinear convergence

AMS subject classification

  • 41A20
  • 65D15
  • 90C32
  • 90C34