Semilocal convergence conditions for the secant method, using recurrent functions. (English) Zbl 1289.65136

Argyros, Ioannis K.; Hilout, Said

Rev. Anal. Numér. Théor. Approx. 40, No. 2, 107-119 (2011).

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.

Reviewer: Hang Lau (Montreal)

MSC:

65J15	Numerical solutions to equations with nonlinear operators (do not use 65Hxx)
47J25	Iterative procedures involving nonlinear operators

Keywords:

recurrent functions; semilocal convergence; secant method; Banach space; majorizing sequence; nonlinear operator equation; numerical examples