2.9.8 Symbolic Intervals

The most general choice of f is to allow arbitrarily complex functions. Another way to view this is to have f as a universal function with an infinite number of coefficients:

Of course, at any point in a computation only a finite number of coefficients are non-zero. A method of this form could completely avoid any difficult decisions by just ``pushing'' the computation into the interval symbolically, as shown in the example following.

Consider using such a system with our simple algorithm for determing a function's range over a given domain. An example problem instance is to determine the range of ,

over the domain [0,1]. The algorithm would proceed as follows:

Although the algorithm returned a description of the tightest bounds possible on the range of g, the results are obviously not of much use. We are no further along than when we started.

Symbolic computation is not a panacea. Although the operator models and demotion operators would be trivial to implement, interpreting the results becomes difficult. Symbolic simplification could be performed by the interval operators.

Jeff Tupper

March 1996