PyRDMIA: um pacote intervalar para aritmética RDM

Abstract

In the work with numerical data in computational environment, some problems have to be faced as a consequence of the limitation that the machine has in representing these values. Because the computer operates on floating-point arithmetic, numerical quantities are approximated to representable machine numbers, thus generating errors that can lead to incorrect results. Moreover, the quantities have an intrinsic uncertainty from the equipment used to determineitor from the operator. This shows that it cannot be said as to the accuracy of a result value generated after a sequence of operations. An alternative to the errors generated by floating-point arithmetic is in the representation of numbers by means o fintervals. It can be done with the use of intervalarithmetic, hich provides automatic error control, besides which interval results carry the guarantee of their uncertainty. Applied in several areas, interval arithmetic began in 1966 with what is now called standard interval arithmetic (SIA), developed by Moore. However, the work with intervals is not a simple task and the search for the solution of failures and insufficiencies of SIA has made that new definitions for the interval arithmetic were developed. The most modern definition for the use of intervals is the arithmetic RDM (Relative Distance Measure). With an approach that differs from other definitions for the use of intervals as an alternative to the use of point values, RDM-IA (Relative Distance Measure - Interval Arithmetic) introduces a variable as an element to represent and treat the uncertainty of numerical values. There are few applications that use RDM-IA where, for these, only theoretical approaches have been employed.There are few applications that use RDM-IA where, for these, only theoretical approaches have been employed. Scientific computation has as one of its objectives the construction of technical solutions for the analysis and resolution of scientific problems, but for that an interface is necessary that allows the application of the solution to the problem in a generic way. In view of this, the present work shows the multidimensional RDM arithmetic in its state of the art with respect to concepts and applications to, from then on, present the development of an interval package in Python programming language that contemplates this definition, making possible its application in algorithms in the search of solutions to problems involving numerical computation.