bisseção

Bisseção, also known as the bisection method, is a root-finding algorithm used in numerical analysis. It is a simple and robust method that works by repeatedly narrowing down an interval that contains a root of a continuous function. The method relies on the Intermediate Value Theorem, which states that if a continuous function has values of opposite signs at the endpoints of an interval, then it must have at least one root within that interval.

The bisection method begins with an initial interval [a, b] such that f(a) and f(b) have opposite signs. The midpoint of the interval, c = (a + b) / 2, is then calculated. If f(c) is zero, then c is the root. If f(c) has the same sign as f(a), then the root must lie in the interval [c, b], and the new interval becomes [c, b]. If f(c) has the same sign as f(b), then the root must lie in the interval [a, c], and the new interval becomes [a, c]. This process is repeated iteratively, with the interval shrinking by half in each step, until the desired level of accuracy is achieved.

The bisection method is guaranteed to converge to a root, provided that the initial interval is chosen correctly and the function is continuous. However, it is a relatively slow method compared to others like Newton's method, especially when high precision is required. Its main advantage lies in its simplicity and guaranteed convergence, making it a reliable choice for many applications. It is often used as a teaching tool to introduce numerical root-finding techniques.