Abstract
The aim of this chapter is to provide an overview of theoretical results and numerical tools in some iterative schemes to approximate solutions of nonlinear equations. Namely, we examine the concept of iterative methods and their local order of convergence, numerical parameters that allow us to assess the order, and the development of inverse operators (derivative and divided differences). We also provide a detailed study of a new computational technique to analyze efficiency. Finally, we end the chapter with a consideration of adaptive arithmetic to accelerate computations.
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Grau-Sánchez, M., Noguera, M. (2016). On Convergence and Efficiency in the Resolution of Systems of Nonlinear Equations from a Local Analysis. In: Amat, S., Busquier, S. (eds) Advances in Iterative Methods for Nonlinear Equations. SEMA SIMAI Springer Series, vol 10. Springer, Cham. https://doi.org/10.1007/978-3-319-39228-8_10
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