A Quasi-newton Method for Solving Small Nonlinear Systems of Algebraic Equations

Finding roots of nonlinear algebraic systems is paramount to many applications in applied mathematics because the physical laws of interest are usually nonlinear. If the functions comprising a system are complicated it is beneficial to reduce computing the functions as much as possible. The following describes a quasi-Newton root solver called Broyden Approximate Norm Descent, or ’BroydenAND’, which can employ either Broyden’s first or second methods, and is shown to be overall less expensive in terms of function evaluations than several competing root solvers. The results for Broyden’s first and second methods are identical for all but the last test function, for which the two methods start to diverge in the presence of round-off errors.