A family of Halley–Chebyshev iterative schemes for non-Fréchet differentiable operators |
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Authors: | Sergio Amat Concepción Bermúdez Sonia Busquier Driss Mestiri |
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Institution: | 1. Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Spain;2. Ecole Superieure de Mecanique de Marseille, Spain |
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Abstract: | A modification of some classical third order methods is studied. The main advantage of these methods is that they do not need evaluate any Fréchet derivative. A convergence theorem in Banach spaces, just assuming that the second divided difference is bounded by a nondecreasing function and a punctual condition, is presented. Fréchet differentiability is not required. Finally, a particular example is analyzed where our conditions are fulfilled and the classical ones fail. |
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