Solving Systems of Equations

Finding solutions of systems of equations is a classical problem. Nowadays, there are even methods for enclosing all real solutions of a given system of equations. Those methods systematically exclude regions that provable do not contain solutions. One method for doing so (the interval Newton method) works with all variables and equations at the same time, another one (Box consistency) first relaxes the system to several univariate equations, and then works with those univariate equations separately. However, intermediate methods would also be conceivable, for example, methods that first relax the full system to a systems of two equations in two variables and then use the interval Newton method on the resulting systems of dimension two. In the thesis, the student will study the feasibility of such an approach using computational experiments.