Comparing Solvers for Large Systems of Nonlinear Algebraic Equations

The solution of systems of nonlinear algebraic equations is a problem which complexity grows as the number of equations increases. The number of engineering problems, which led to these systems, is increasing each year. In this paper we compare the performance of four advanced solvers for systems of nonlinear algebraic equations which have been collected from Internet repositories. We are particularly interested in their performance when the number of equations is large (100+). We have collected test problems from literature and the Internet and found that most popular problems consist of systems of 2-4 equations but a few of the popular test problems are defined in such a way that they can be extended to a large system of nonlinear algebraic equations. In the paper we report on results of our experiments in applying the nonlinear solvers to these test problems for an increasing number of equations. All of the solvers that we are using were designed to handle small and medium sized (up to 100) problems. Since the source code was available we were able to extend their functionality to handle problems with up to 200 equations and test the solvers’ efficiency by comparing their convergence rates and sensitivity to starting vectors. In the paper, we first describe the solvers and the algorithms on which the solvers are based. This is followed by the presentation of our experimental results. We end our discussion with conclusions and a description of future research directions.