5. Root Finding with Bracketing Methods

Bisection Method

Bisection method based on the Intermediate Value Theorem, which states that if the function is continuous on an interval [a,b] and changes sign over that interval, then there exists at least one root in the interval.

Condition

The lower a and upper b bounds should be selected as the function changes sign over the interval. This condition can be checked by ensuring the following inequality:

$$f(a) \cdot f(b) < 0$$