On a secant-like method for solving generalized equations. (English) Zbl 1199.65182

Argyros, Ioannis K.; Hilout, Saïd

Math. Bohem. 133, No. 3, 313-320 (2008).

Summary: S. Hilout and A. Piétrus [Positivity 10, No. 4, 693–700 (2006; Zbl 1118.47052)] had given a semilocal convergence analysis for a secant-like method to solve generalized equations using Hölder-type conditions introduced by the first author (for nonlinear equations). Here, we show that this convergence analysis can be refined under weaker hypothesis, and less computational cost. Moreover, finer error estimates on the distances involved and a larger radius of convergence are obtained.

MSC:

65J15	Numerical solutions to equations with nonlinear operators
47J25	Iterative procedures involving nonlinear operators

Keywords:

secant-like method; generalized equations; Aubin continuity; radius of convergence; divided difference; error estimates

Citations:

Zbl 1118.47052