On the convergence of Broyden’s method in Hilbert spaces

In this paper, we present a new semilocal convergence analysis for an inverse free Broyden’s method in a Hilbert space setting. In the analysis, we apply our new idea of recurrent functions concepts of divided differences of order one and Lipschitz/center–Lipschitz conditions on the operator involved. Our analysis extends the applicability of Broyden’s method in cases not covered before. Finally, we give an example to illustrate the main result in this paper.