Algorithm 748: Enclosing Zeros of Continuous Functions

@article{Alefeld1995Algorithm7E,
  title={Algorithm 748: Enclosing Zeros of Continuous Functions},
  author={G{\"o}tz Alefeld and Florian A. Potra and Yixun Shi},
  journal={ACM Trans. Math. Softw.},
  year={1995},
  volume={21},
  pages={327-344}
}
Two efficient algorithms for enclosing a zero of a continuous function are presented. They are similar to the recent methods, but together with quadratic interpolation they make essential use of inverse cubic interpolation as well. Since asymptotically the inverse cubic interpolation is always chosen by the algorithms, they achieve higher-efficiency indices: 1.6529… for the first algorithm, and 1.6686… for the second one. It is proved that the second algorithm is optimal in a certain family… CONTINUE READING
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Same efficient methods for enclosing simple zeros

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Two efficient aIgorithms with guaranteed convergence for finding a zero of a function

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