Parameter selection rules for path-following with singular embedding

Singular embedding methods require appropriately adjusted parameters to gua rantee the contraction of locally quadratically convergent iterative method s. Firstly some general rule for the parameter selection is proposed and it s rate of convergence is analyzed. Secondly, some modifications in the case of polynomial error and contraction bounds are studied. Finally, these res ults are applied to the embedding of an elliptic boundary value problem wit h discontinuous nonlinearities into a family of smooth problem:;. Here the regularization is done in such a way that the solutions of the resulting au xiliary problems require only one step of Newton's method.