With the converging interval representation, generalized interval arithmetic can be used for real arithmetic. Better convergence can be realized using generalized interval arithmetic rather than constant interval arithmetic. This will be argued later, but as a trivial example consider symbolic intervals. With symbolic intervals, convergence is immediate although unproductive.
Generalized interval arithmetic provides functional bounds for expressions. These functional bounds will be exploited by the geometric algorithms presented in later chapters. Conventional real number representations do not provide information as to the effect expression parameters have on evaluated expressions.
| Jeff Tupper | March 1996 |