Interval Analysis

4Expressions, P-contraction, ε-inflation

4.1Expressions, range

In Section 2.6 we defined the elementary interval functions by their range. This definition could also be applied for general continuous functions f : D ⊆ ℝⁿ → ℝ since such functions assume their maximum and minimum on each compact set, particularly on each interval vector [x] ⊆ D. Unfortunately, in most cases neither these extrema nor their position can be easily determined. Therefore, one replaces these optimal definitions by a coarser one such that the resulting image for an input [x] encloses at least the range R_f([x]) of f restricted to [x] ⊆ D. To this end we define a certain set 𝔼 of admissible expressions and the interval arithmetic evaluation of their induced functions which ...