On the dependency problem when approximating a solution set of a system of nonlinear inequalities

In this paper, the interval analysis and the nonuniform covering approach are used to solve systems of nonlinear inequalities. We discuss two approaches to getting extreme value approximations for every function of the system and for every box of the covering. One approach is based on the idea that the system should be simplified to get rid of multiple occurrences of an interval in an inequality. Another one is the straightforward approach without system manipulations that is used the initial system and the interval analysis to get the extreme approximations. We juxtapose the results to find the difference between the approaches based on the number of iterations needed to get the approximation. The results show that the approach with system simplification gives better approximations and uses less iterations to get the solution.