Bisection Method
The bisection method finds a root on an interval [a,b] where f(a)f(b)<0 by repeatedly halving at the midpoint; it converges linearly but is absolutely reliable.
Purpose
To provide a guaranteed-convergent, robust root-finding method for continuous functions.
Mechanism
Let c=(a+b)/2; if f(a)f(c)<0 the root lies in [a,c], otherwise in [c,b]. Each step halves the interval, with error ≤(b-a)/2^n. It requires f continuous and endpoints of opposite sign. Slow but reliable convergence.
Use cases
- Equation root finding
- Robust numerical methods
- Interval search