Question

Consider the bisection method to find a root for f(x) = 0 where f is a continuous function. We take the [0, 1] as the initial interval provided that f(0)f(1) < 0. We take the following practical stopping criteria: |bn − an| ≤ , = 1 × 10−8 . How many steps of the bisection method are needed to obtain an approximation to the root?

Answer 1

Answer: It would take approximately 27 steps to obtain an approximation of the root.

Step-by-step explanation: The bisection method is a numerical procedure to find a root to a equation continuous in an interval [a.b]. It consists in repeatedly halve the interval [a,b], keeping the half for which f(x) changes sign. The repetition will continue until a stopping criteria is reached. To find how many interactions is necessary, we can satisfy the equation:

`(1)/(2^(n) )` · (b - a) ≤ ε, where a and b are the original interval and ε is the stopping criteria.

Substituting the parameters and using log 2 = 0,301, the number of iterations needed is approximately 27.