4.2.7 Linear Interval Arithmetic

Let denote a two-dimensional linear interval arithmetic, such as or . We will not ensure that R represents directly; we will instead work with . The interval specification is computed by evaluating the specification S using the interval arithmetic . The interval inclusion property assures us that

Let describe , using an element of :

We may then determine by considering

for . The remaining sections detail how may be determined. We account for the domain of S as before.

Other linear interval arithmetics may be used, such as or , given an appropriate . Better renderings may be obtained by taking S into account when choosing and .

Jeff Tupper

March 1996