Solvers for Nonlinear Algebraic Equations: Where Are We Today?

The aim of this paper is to summarize the state-of-the-art in solving systems of nonlinear algebraic equations. We are interested in two aspects of the problem. First, the existing solvers and their robustness. Second, the existing test-problem libraries and their adequacy. We explore both issues from the engineering-oriented perspective (e.g. by approaching the solvers as black-box software). Experimental data illustrating our main points is presented and discussed