![]() if f(c) = 0 means that we found the root of the function, which is c.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) has the same sign as f(b), we replace b with c and we keep the same value for a.and recalculate c with the new value of a or b The algorithm ends when the values of f(c) is less than a defined tolerance (e.g. In this case we say that c is close enough to be the root of the function for which f(c) ~= 0. In order to avoid too many iterations, we can set a maximum number of iterations (e.g. Image: The Bisection Method Explained as a Logic Diagramġ000) and even if we are above the defined tolerance, we keep the last value of c as the root of our function. ![]() ![]() ![]() 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. 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. ![]()
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