Optimal Order of One-Point and Multipoint Iteration

  title={Optimal Order of One-Point and Multipoint Iteration},
  author={H. T. Kung and Joseph F. Traub},
  journal={J. ACM},
The problem is to calculate a simple zero of a nonlinear function ƒ by iteration. There is exhibited a family of iterations of order 2<supscrpt><italic>n</italic>-1</supscrpt> which use <italic>n</italic> evaluations of ƒ and no derivative evaluations, as well as a second family of iterations of order 2<supscrpt><italic>n</italic>-1</supscrpt> based on <italic>n</italic> — 1 evaluations of ƒ and one of ƒ′. In particular, with four evaluations an iteration of eighth order is constructed. The… Expand
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  • Computer Science, Mathematics
  • ACM National Meeting
  • 1961
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  • Computer Science
  • SIAM J. Comput.
  • 1972
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  • SIAM J . Numer . Anal .
  • 1973
Optimal order for iterations using two evaluations
  • Report, Computer Sci. Dep. , Carnegie-Mellon U., Pittsburgh,
  • 1973