The bisection method (or method of interval halving) offers somewhat faster convergence than incremental search. Unlike the latter method, however, the bisection method requires prior knowledge of upper and lower bounds to the root, say. (These bounds can be determined using an incremental search routine with a relatively coarse step size, for example.)

Having bounded the root between these two points, we evaluate the function y at the midpoint, i.e. . By definition, the root must lie either in the interval or the interval . The proper interval is determined by checking the sign of the quantity . If this value is negative, the root lies within the interval ; otherwise, the root must lie in the interval . This process of halving the interval and identifying the subdomain containing the root is repeated until the interval is smaller than some prescribed tolerance.