# Dichotomous search

### From Glossary

This finds the maximum of a unimodal function on an interval, , by evaluating points placed near the center, approximating the bisection method. With being a small positive value, let and . Then, if , the new interval of uncertainty is ; if , it is ; if , it is . With function evaluations, the interval of uncertainty can be reduced to within , where

The same reduction occurs with , as an even number of evaluations is required. For example, with , , so the interval reduction is . See fibonacci search for a more efficient method.