My master thesis concerns itself with the improvement of the convergence behavior of two algorithms.
I firstly examen and propose improvements to the Newton-Raphson root-finding algorithm. Then, I make comparison between the improved and standard methods.
Secondly, a standard minimization algorithm, called the Gauss-Newton method, is covered. I propose a change which aims to improve the convergence of the algorithm when dealing with with noisy data.
Finally, I present the results of both improvements and apply the new methods to a simple 1D non-linear FEM problem.