The W4 method: a new multi-dimensional root-finding scheme for nonlinear systems of equations
For researchers and practitioners solving nonlinear systems, this method offers a more robust alternative to Newton-Raphson with improved global convergence, though it is an incremental improvement.
The authors propose a new multi-dimensional root-finding method for nonlinear systems, inspired by damped oscillators, which extends the Newton-Raphson method. It achieves the same local convergence rate but with a significantly wider convergence region, as demonstrated on several examples.
We propose a new class of method for solving nonlinear systems of equations, which, among other things,has four nice features: (i) it is inspired by the mathematical property of damped oscillators, (ii) it can be regarded as a simple extention to the Newton-Raphson(NR) method, (iii) it has the same local convergence as the NR method does, (iv) it has a significantly wider convergence region or the global convergence than that of the NR method. In this article, we present the evidence of these properties, applying our new method to some examples and comparing it with the NR method.