Third-order iterative methods without using any Fréchet derivative

Authors:
Sergio Amat;Sonia Busquier;Vicente Candela
Affiliations:
Departamento de Matemática Aplicada y Estadistica, Universidad Politécnica de Cartagena, Paseo de Alfonso XIII, 52 Cartagena 30203, Spain;Departamento de Matemática Aplicada y Estadistica, Universidad Politécnica de Cartagena, Paseo de Alfonso XIII, 52 Cartagena 30203, Spain;Departament de Matemàtica Aplicada, Universitat de València, Spain
Venue:
Journal of Computational and Applied Mathematics - Special issue: Selected papers from the conference on computational and mathematical methods for science and engineering (CMMSE-2002) Alicante University, Spain, 20-25 september 2002
Year:
2003

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Abstract

A modification of classical third-order methods is proposed. The main advantage of these methods is they do not need to evaluate any Fréchet derivative. A convergence theorem in Banach spaces, just assuming the second divided difference is bounded and a punctual condition, is analyzed. Finally, some numerical results are presented.