Determining zeroes of increasing Lipschitz functions

Summary We study the average case behavior of suitable algorithms to solve a nonlinear problem in numerical analysis: determining zeroes of increasing Lipschitz functions of one variable. The bisection method (which is optimal with respect to the maximal error over the whole class of functions) is far from being optimal in a more general sense: There are methods which behave like bisection in the worst case but which yield much better results on the average. We prove that the sequentially optimal algorithm found by Sukharev is also optimal in our average case setting.