Effective Evaluation of Hausdorff Distances for Finite Unions of Hyperrectangles

Effective Evaluation of Hausdorff Distances for Finite Unions of Hyperrectangles. Based on the usual Operations, relations and evaluations of function values for axis-parallel hyperrectangles, the corresponding objects for finite sets of hyperrectangles resp. their unions can be defined and implemented in a natural way. Algebraic properties remain valid. The aim of this paper is to give also methods for an effective evaluation of lower and upper distances as well as of Hausdorff distances for such sets. On this basis the distances and similarity and congruency grades for each pair of nonempty bounded subsets of ℝn are approximately computable, and the convergence behaviour of general set-valued iteration processes can be investigated.