An interval method for global nonlinear analysis

In this paper, the problem of finding the set of all real solutions to a system of n nonlinear equations contained in a given n-dimensional box [the global nonlinear analysis (GNA) problem] is considered. A new iterative interval method for solving the GNA problem is suggested. It is based on the following techniques: (1) 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; (2) enclosure of the nonlinear augmented system at each iteration by a specific linear interval system of size n'×n'; (3) elimination of the auxiliary variables; and (4) solution of the resulting reduced size n×n linear system, using the so-called constraint propagation approach. The method suggested shows a significant improvement over previous techniques for the numerical examples solved