Solving Nonlinear Systems by Constraint Inversion and Interval Arithmetic

A reliable symbolic-numeric algorithm for solving nonlinear systems over the reals is designed. The symbolic step generates a new system, such the formulas are different but the solutions are preserved, through partial factorizations of polynomial expressions, and constraint inversion. The numeric step is a branch-and-prune algorithm based on interval constraint propagation to compute a set of outer approximations of the solutions. The processing of the inverted constraints by interval arithmetic provides a fast and efficient method to contract the variables’ domains. A set of experiments for comparing several constraint solvers is reported.