Effective Representation and Fast Computing With Polyarc Bounded Intervals

Abstract

Complex interval arithmetic is a powerful tool for the analysis of computational errors. The naturally arising rectangular, polar, and circular interval types yield overly relaxed bounds. The later introduced polygonal type allows for arbitrarily precise representation for a higher computational cost. We propose the polyarcular interval type as an effective generalization of the above-mentioned types. The polyarcular interval can represent all types and most of their arithmetic combinations precisely and has a better approximation capability with that of the polygonal interval. In particular, in specific cases of antenna tolerance analysis and robot localization it can achieve perfect accuracy for lower computational cost then the polygonal type, which we show in a relevant case study.