A Bisection Method Like Algorithm for Approximating Extrema of a Continuous Function

For a continuous function $f$ defined on a closed and bounded domain, there is at least one maximum and one minimum. First, we introduce some preliminaries which are necessary through the paper. We then present an algorithm, which is similar to the bisection method, to approximate those maximum and minimum values. We analyze the order of the convergence of the method and the error at the $k$-th step. Then we discuss the pros and cons of the method. Finally, we apply our method for some special classes of functions to obtain nicer results. At the end, we write a Matlab script which implements our algorithm.