What is the Bisection method and how do you use it?I am taking a test on this next week and I need verification on what the Bisection method is. 



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Posted on (Answer #1)

The Bisection Method is a numerical method for estimating the roots of a polynomial f(x). It is one of the simplest and most reliable but it is not the fastest method. Assume that f(x) is continuous.

Algorithm for the Bisection Method: Given a continuous function f(x)

  1. Find points a and b such that a < b and f(a) * f(b) < 0.
  2. Take the interval [a, b] and find its midpoint x1.
  3. If f(x1) = 0 then x1 is an exact root, else if f(x1) * f(b) < 0 then let a = x1, else if f(a) * f(x1) < 0 then let b = x1.
  4. Repeat steps 2 & 3 until f(xi) = 0 or |f(xi)| <= DOA, where DOA stands for degree of accuracy.

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