Semilocal Convergence of a Newton-Secant Solver for Equations with a Decomposition of Operator

Abstract

We provide the semilocal convergence analysis of the Newton Secant solver with a decomposition of a nonlinear operator under classical Lipschitz conditions for the first order Fr´echet derivative and divided differences. We have weakened the sufficient convergence criteria, and obtained tighter error estimates. We give numerical experiments that confirm theoretical results. The same technique without additional conditions can be used to extend the applicability of other iterative solvers using inverses of linear operators. The novelty of the paper is that the improved results are obtained using parameters which are special cases of the ones in earlier works. Therefore, no additional information is needed to establish these advantages.