Although floating point computations are simple and efficient, rounding can cause a stream of floating point computations to quietly diverge from the envisioned stream of real computations. Interval arithmetic guarantees rigorous results yet is built from floating point arithmetic. Interval arithmetic will not prevent a series of computations from wandering but it will inform the user how much the computed result could deviate from the real result (the result using real numbers for the computations). The presentation given here differs somewhat from conventional introductions [4, 56, 57], due to the impending generalizations.
The set of intervals is denoted by . An interval is specified by two floating point numbers, a lower and upper bound.
For example, can be represented as the interval
|Jeff Tupper||March 1996|