EXPANDING THE APPLICABILITY OF A TWO STEP NEWTON LAVRENTIEV METHOD FOR ILL-POSED PROBLEMS - Argyros, I. K.; George, S. (Journal of Nonlinear Analysis and Optimization: Theory & Applications (JNAO), 2013)
In [3] we presented a cubically convergent Two Step Directional NewtonMethod (TSDNM) for approximating a solution of an operator equation in a Hilbert space setting. George and Pareth in [13] use the analogous Two Step Newton Lavrentiev Method (TSNLM) to approximate a solution of an ill-posed equation. In the present paper we show how to expand the applicability of (TSNLM). In particular, we present a semilocal convergence analysis of (TSNLM) under: weaker hypotheses, weaker convergence criteria, tighter error estimates on the distances involved and an at least as precise information on the location of the solution.