Provided that the initial interval bounds a root and the function is well-behaved, the bisection method is guaranteed to find it. Like incremental search, the bisection method yields an accurate upper limit on the error: . While the method's rate of convergence is improved over that of incremental search, it is slower than other techniques. In fact, the bisection method converges at a linear rate, so that the error at iteration n+1, , is related to the error associated with the previous iteration, , according to the relationship

where is some constant less than 1.

In fact, a linear rate of convergence isn't all that bad – it's just slower than that of other (less reliable) procedures.