$$\omega$$-conditioned divided differences to solve nonlinear equations.(English)Zbl 1056.47055

Madaune-Tort, M. (ed.) et al., 7th Zaragoza-Pau conference on applied and statistical mathematics, Jaca (Huesca), September 17–18, 2001. Zaragoza: Univ. de Zaragoza, Seminario Matemático “García de Galdeano” (ISBN 84-96214-04-4/pbk). Monogr. Semin. Mat. “García de Galdeano” 27, 323-330 (2003).
Some iterative secant-type processes are used to solve nonlinear equations. The semi-local convergence of these is studied via generalized $$(k,p)$$-Hölder continuity and $$\omega$$-conditioned divided differences.
For the entire collection see [Zbl 1024.00039].

MSC:

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