Symbolic preprocessing in interval function computing

Abstract

Symbolic manipulation proved to be a very efficient tool for detection and removal of dependency relations between variables : it is completed at the end of the global simplification. On the other hand the reduction to 1 (or 0) of the number of occurrences of variables is closely related to the structure of the expressions themselves. It is in general not achieved at the local simplification level. The limited possibilities for reduction and the varying character of expressions, just to mention two aspects, mean that we never can be sure to have been producing the best computable form for an expression (if existing) but only a more suitable one. However even a small gain at the symbolic level has very important repercussions for the quality of the computed results : any reduction of the number of elementary operations will not only improve the execution time, but also the accuracy of the final result.

Performing rigourous computations with strongly noised data may be a reasonable venture towards a good balance between symbolic and numerical calculations.