Finding and verifying all solutions of a system of nonlinear equations using public domain software: Working paper series--02-14
Max E. Jerrell, Wendy A. Campione · 2002
Economic models are often stated as systems of nonlinear equations, for example general equilibrium models, game theory models, and macroeconomic models. The existence and uniqueness of solutions to the model are critical issues. Interval arithmetic is an arithmetic that operates on interval values rather than point values. It can be used to find all solutions of a system of nonlinear equations over a specified region and to determine if a solution is unique. We present arguments demonstrating that this arithmetic is capable of determining existence and uniqueness. We then use a public domain software package to find all roots of several simple economic example problems.