Optimale nullstellensuche bei vorliegen einer apriori-verteilung

Abstract

In this paper, the search for the zero of a monotone decreasing function f ∣ [a, b] → R ¹ with f(a) > 0, f(b)↪ 0 is treated. Here f is known as far as f(x) can be found x ∈ [a, b]. I t is supposed that f has exactly one zero and there exists a prior information of its position in form of a probability distribution on [a, b]. The problem is formulatedas a bne of process control where the sum of lengths of intervals excluded of further search is used as regard functional. Starting from BELLMAN'S equation of stochastic dynamic programming formulae for determination of an optimal or ssymptotic optimal n-step strategy are given. Finally. additional costs c per search step are considered.