Bisection Method (Internal Halving Method)

This method is based upon the use of the intermediate mean-value theorem which states that for a continuous function f, defined on the closed interval [a, b], with f(a) and f(b) having opposite signs, there exists at least one number x such that ax ₁ be the mid-point of [a, b]. If x ₁ satisfies Equation (7.2 1), x ₁ is the required root. If not, f(x ₁) has the same sign as either f(a) or f(b). If f(x ₁) and f(a) have the same sign, the required root lies in the interval (x ₁, b), as illustrated in Figure 7.2 1. We then proceed to find the mid-point of (x ₁, b). Similarly if f(x ₁) and f(b) have the same sign, the required root lies in the interval (a, x ₁) and in this case x ₂