![]() 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 if f(c) has the same sign as f(b), we replace b with c and we keep the same value for a.if f(c) has the same sign as f(a) we replace a with c and we keep the same value for b. ![]() if f(c) = 0 means that we found the root of the function, which is c.the function f is evaluated for the value of c.interval halving: a midpoint c is calculated as the arithmetic mean between a and b, c = (a + b) / 2.two values a and b are chosen for which f(a) > 0 and f(b) For a given function f(x),the Bisection Method algorithm works as follows:
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