After evaluating the function in both points we can see that f(a) is positive while f(b) is negative. In the table below we are going to calculate the values described in the logic diagram above: iĪt initialization ( i = 0) we choose a = -2 and b = 5. The best way of understanding how the algorithm work is by looking at an example.įor the function f(x) below find the best approximation of the root given the tolerance of TOL = 0.01 and a maximum of NMAX = 1000 iterations.
Image: The Bisection Method Explained as a Logic Diagram 1000) and even if we are above the defined tolerance, we keep the last value of c as the root of our function. In order to avoid too many iterations, we can set a maximum number of iterations (e.g. In this case we say that c is close enough to be the root of the function for which f(c) ~= 0. The algorithm ends when the values of f(c) is less than a defined tolerance (e.g. and recalculate c with the new value of a or b
For a given function f(x),the Bisection Method algorithm works as follows:
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