sets the lower bound for the function domain
This method sets the maximum number of function evaluations for the bracketing routine. An error is thrown if a bracket is not found after this number of evaluations.
sets the upper bound for the function domain
This method returns the zero of the function $ f $, determined with the given accuracy $ \epsilon $; depending on the particular solver, this might mean that the returned $ x $ is such that $ |f(x)| < \epsilon $ , or that $ |x-\xi| < \epsilon $ where $ \xi $ is the real zero.
This method contains a bracketing routine to which an initial guess must be supplied as well as a step used to scan the range of the possible bracketing values.
This method returns the zero of the function $ f $, determined with the given accuracy $ \epsilon $; depending on the particular solver, this might mean that the returned $ x $ is such that $ |f(x)| < \epsilon $ , or that $ |x-\xi| < \epsilon $ where $ \xi $ is the real zero.
An initial guess must be supplied, as well as two values $ x_\mathrm{min} $ and $ x_\mathrm{max} $ which must bracket the zero (i.e., either $ f(x_\mathrm{min}) \leq 0 \leq f(x_\mathrm{max}) $, or $ f(x_\mathrm{max}) \leq 0 \leq f(x_\mathrm{min}) $ must be true).
The implementation of the algorithm was inspired by Press, Teukolsky, Vetterling, and Flannery, "Numerical Recipes in C", 2nd edition, Cambridge University Press
False position 1-D solver
test the correctness of the returned values is tested by checking them against known good results.