Average-case Optimality of a Hybrid Secant-bisection Method

@inproceedings{Novak2010AveragecaseOO,
title={Average-case Optimality of a Hybrid Secant-bisection Method},
author={Erich Novak and Klaus Ritter and Henryk Wozniakowski},
year={2010}
}

We present an average-case complexity analysis for the zerofinding problem for functions from C([0, 1]), r > 2 , which change sign at the endpoints. This class of functions is equipped with a conditional r-folded Wiener measure. We prove that the average-case complexity of computing an «-approximation is of order log log( 1 /e), and that a hybrid secant-bisection method with a suitable adaptive stopping rule is almost optimal. This method uses only function evaluations. We stress that the… CONTINUE READING