An Interval Method for Global Non-linear Analysis

In this paper, the problem of finding the set of all real solutions to a system of n nonlinear general form algebraic equations contained in a given n-dimensional box (the global analysis problem) is considered. A new iterative interval method for solving the global analysis problem is suggested. It is based on the following techniques: (i) transformation of the original system into an augmented system of n n m ' = + equations of n' variables by introducing m auxiliary variables, the augmented system being of the so-called semiseparable form; (ii) enclosure of the nonlinear augmented system at each iteration by a specific linear interval system of size n' x n'; (iii) elimination of the auxiliary variables; (iv) solution of the resulting reduced size n x n linear system, using the so-called constraint propagation approach. The overall efficiency of the method suggested is illustrated by several numerical examples.