Local convergence for a family of third order methods in Banach spaces
نویسندگان
چکیده
S.K. Khattri Department of Engineering Stord Haugesund University College Norway Email: [email protected] Abstract. We present a local convergence analysis of a family of third order methods for approximating a locally unique solution of nonlinear equations in a Banach space setting. Recently, the semilocal convergence analysis of this method was studied by Chun, Stănică and Neta in [10]. These authors extended earlier results by Kou, Li [17] and others [8, ?, 11, 13, 14]. The convergence analysis is based on hypotheses up to the second Fréchet derivative of the operator involved. This work further extends the results of [10] and provides computable convergence ball and computable error bounds under hypotheses only up to the first Fréchet derivative.
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