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A.C. Christiansen, J.C. Morud and S. Skogestad, ``A comparative analysis of methods for solving systems of nonlinear algebraic equations,'' Proc. of the 38th SIMS Simulation Conference, Trondheim, June 1996, 217-230.

Abstract.
This paper compares two numerical methods for finding solutions to a system of non-linear algebraic equations (NAEs). We consider homotopy-continuation methods and discuss inherent difficulties in using such methods. To prevent potential unboundedness of the homotopy paths we provide some insight into how appropriate branch-jumping techniques may be applied. We also present a novel tear and grid method based on conventional techniques of partitioning and precedence ordering, with the addition of including a grid of the tear variables. Both methods may be used to obtain initial solutions as well as exploring solutions in the parameter space. A comparative analysis of the methods is presented in terms of a few example problems. For simple models consisting of a relatively small number of equations, we find that the grid method offers potential savings in both computer time and implementation effort. However, the perhaps most appealing feature of the tear and grid method lies in the convenient visualization of the solution space.