## NRiC 9.1 lists some simple bracketing routines.

## Once bracketed, root is easy to find by

__bisection__:- Evaluate
*f*at interval midpoint (*a*+*b*) / 2. - Root must be bracketed by midpoint and whichever
*a*or*b*gives*f*of opposite sign. - Bracketing interval decreases by 2 each iteration:
*n*+1 =*n*/ 2.

- Hence to achieve error tolerance of
**starting from interval of size**0 requires*n*= log2(**0/**) steps.

- Evaluate