## Bisection Procedure

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)

so
 (5)

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.