×

zbMATH — the first resource for mathematics

Semilocal convergence conditions for the secant method, using recurrent functions. (English) Zbl 1289.65136
The authors provide sufficient convergence conditions for the secant method to a locally unique solution in solving a nonlinear equation in a Banach space. By using the concept of recurrent functions, and combining Lipschitz and center-Lipschitz conditions on the divided difference operator, the semilocal convergence of the secant method is established. Some numerical examples are presented.

MSC:
65J15 Numerical solutions to equations with nonlinear operators (do not use 65Hxx)
47J25 Iterative procedures involving nonlinear operators
PDF BibTeX XML Cite