2.9.5 Quadratic Intervals

Rather than using linear bounds for the intervals, quadratic bounds may be used. The quadratic real interval number system is denoted by     :

Each interval u of is specified by two quadratic functions, each of which is specified by three extended real numbers:

Since we require that both the lower and upper bound be well-defined functions, some possible descriptions are never valid. An example is the function , which is not defined for . The methods used to implement interval operators will naturally avoid such descriptions.

Function demotion through and is more difficult than function demotion through and . A later section will describe how function demotion is performed.

Jeff Tupper

March 1996