This article is about searching continuous function values. For searching a finite sorted array, see binary searchalgorithm.A few steps of the bisection methodapplied over the starting range [a1;b1]. Thebigger red dot is the root of the function.The bisection methodin mathematics is a root-finding method that repeatedly bisects aninterval and then selects a subinterval in which a root must lie for further processing. It is avery simple and robust method, but it is also relatively slow. Because of this, it is often usedto obtain a rough approximation to a solution which is then used as a starting point for morerapidly converging methods.The method is also called the interval halvingmethod,thebinary search method,or the dichotomy method.The method is applicable for numerically solving the equation f(x) = 0 for the real variable x,where fis a continuous function defined on an interval [a,b] and where f(a) and f(b) haveopposite signs. In this case aand bare said to bracket a root since, by the intermediate valuetheorem, the continuous function fmust have at least one root in the interval (a, b).At each step the method divides the interval in two by computing the midpoint c= (a+b) / 2 ofthe interval and the value of the function f(c) at that point. Unless cis itself a root (which isvery unlikely, but possible) there are now only two possibilities: either f(a) and f(c) haveopposite signs and bracket a root, or f(c) and f(b) have opposite signs and bracket a root.The method selects the subinterval that is guaranteed to be a bracket as the new interval toThe method
be used in the next step. In this way an interval that contains a zero of fis reduced in width by50% at each step. The process is continued until the interval is sufficiently small.