A new family of multipoint methods of second order.
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Universidad de La Rioja
info
ISSN: 0163-0563
Any de publicació: 1998
Volum: 19
Número: 5
Pàgines: 499-512
Tipus: Article
Altres publicacions en: Numerical Functional Analysis and Optimization
Resum
We introduce a new family of multipoint methods of R-order two to approximate a solution of nonlinear operators equation in Banach spaces. An existence-uniqueness theorem and error estimates are provided for this family of iterations using Newton-Kantorovich-type assumptions and a technique based on a new system of recurrence relations. For a special choice of the parameter involved, we obtain the Midpoint method, whose order of convergence is three.