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Local convergence of an at least sixth-order method in Banach spaces. (English) Zbl 1412.65036

Summary: We present a local convergence analysis of an at least sixth-order family of methods to approximate a locally unique solution of nonlinear equations in a Banach space setting. The semilocal convergence analysis of this method was studied by S. Amat et al. [Appl. Math. Comput. 206, No. 1, 164–174 (2008; Zbl 1157.65369); Appl. Numer. Math. 62, No. 7, 833–841 (2012; Zbl 1387.65049)]. This work provides computable convergence ball and computable error bounds. Numerical examples are also provided in this study.

MSC:

65J15 Numerical solutions to equations with nonlinear operators
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