How can the Newton-Raphson method (that is, the multivariate generalization of Newton's method, used in the solution of nonlinear systems) be improved so as to attain better convergence? As-is, in most cases a fairly good initial value is required to ensure convergence.
Note that I'm aware other method exist. Here, I'm simply interested in alterations/modifications to Newton's method.
If you want faster than Newton, the next step is Halley method.
It is amazing since, on yesterday, I found a very recent paper on this topic (which is also among my concerns).
For Householder, another paper.