Given an interval , let and be the endpoints at the th iteration and be the th approximate
solution. Then, the number of iterations required to obtain an error smaller than is found as follows.

(1) |

(2) |

(3) |

(4) |

(5) |

**References**

Arfken, G. *Mathematical Methods for Physicists, 3rd ed.* Orlando, FL: Academic Press, pp. 964-965, 1985.

Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. ``Bracketing and Bisection.'' §9.1 in
*Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed.* Cambridge, England:
Cambridge University Press, pp. 343-347, 1992.

© 1996-9

1999-05-26