BISECTION
Is a root-finding method that applies to any continuous functions for which one knows two values with opposite signs.
The method consists of repeatedly bisecting the interval defined by these values and then selecting the subinterval in which the function changes sign, and therefore must contain a root. It is a very simple and robust method, but it is also relatively slow.
Each iteration performs these steps:
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Calculate c, the midpoint of the interval, c = a + b/2.
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Calculate the function value at the midpoint, f(c).
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If convergence is satisfactory (that is, c - a is sufficiently small, or |f(c)| is sufficiently small), return c and stop iterating.
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Examine the sign of f(c) and replace either (a, f(a)) or (b, f(b)) with (c, f(c)) so that there is a zero crossing within the new interval.
A few steps of the bisection method applied over the starting range [a1;b1]. The bigger red dot is the root of the function.