Definição da exponencial na aritmética intervalar RDM e aplicação em problemas com distribuição de probabilidade

Abstract

Numerical problems in digital systems happen due to their characteristic operate on the set of real numbers, forcing them to discretize this set by means of truncations and rounding. Due to machine constraints, it is not always possible to represent floating point values exactly. Interval arithmetic emerged as tool that allows the solution of these numerical problems, treating inaccuracies and providing an automatic error control, by approaching a real number by a range with upper and lower limits. However, Moore’s interval arithmetic model has some limitations, such as the excess width of this interval and dependence on data. In order to correct these and other problems the Relative-Distance- Measure (RDM) interval arithmetic was developed. Current works prove that this new arithmetic returns more accurate results when compared to Moore. The objective of this work is to define the natural exponential for RDM arithmetic and to apply probabilities with probability distribution hoping to obtain more exact results. Finally, we verified the quality of the results obtained by applying quality metrics to the intervals resulting from the applications developed with the integration methods of Rall, Bedregal and Simpson Intervalar, as well as the comparison of these results among the arithmetic of Moore and RDM and complexity analysis of the exponential RDM that was defined in this work.