Optimal choice of linear interval extension

摘要

A basic problem in interval analysis is to find more accurate interval extension of a function on a given interval. The more accurate interval extension is, the less computation is needed in the solution of a problem, and the more useful the analysis is in other applications. As the first step, this paper investigates the optimal choice of linear interval extension. It is found that one only needs to calculate function values at two particular points in order to find the optimal interval extension generated by linear interval extensions.