  System identification is an important area of science, which aims to describe
the characteristics of the system, representing them by mathematical models.
Since many of these models can be seen as recursive functions, it is extremely
important to control the errors in these functions, because small errors
introduced in each computational step can grow exponentially due to the
sensitivity to initial conditions present in this type of functions. One of the
ways to control rounding and truncation errors is through interval arithmetic,
since it is not possible to represent all numbers in the computer because of
the finite representation in them. Thus, in arithmetic interval a number is
represented by an interval in which the true number is within that interval. In
this manuscript we developed an algorithm that performs the operations of
interval arithmetic using basic functions. We have compared compared our
results with the Matlab-toolbox Intlab. Numerical experiments have shown that
our method is superior producing narrower intervals.
