Mata routines for solution of nonlinear systems using interval methods

Solution of nonlinear systems has become increasingly important as a step in many estimation problems, and is a problem of interest in its own right. I introduce a collection of Mata routines that can be used to find all solutions to nonlinear equation systems, and demonstrate their usage on a sequence of test problems. While specifically tailored to solving polynomial systems, the method can be applied to any continuous system with continuous Jacobian. The methods rely on interval Newton methods, a technique which combines Taylor expansion, bisection, and interval programming. The routines come equipped with an heuristic solver that allows for approximate solution of problems that are especially time consuming, or problems that do not require that all solutions be found. Support tools for the solver include functions for interval arithmetic and manipulation of series of matrices in parallel. I discuss an extended application of the solution tools to the problem of finding all equilibria of discrete action games, which in general requires solving polynomial systems.