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On Convergence and Efficiency in the Resolution of Systems of Nonlinear Equations from a Local Analysis

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Advances in Iterative Methods for Nonlinear Equations

Part of the book series: SEMA SIMAI Springer Series ((SEMA SIMAI,volume 10))

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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Author information

Authors and Affiliations

  1. Department of Mathematics, Technical University of Catalonia ⋅ BarcelonaTech, Campus Nord, Edifici Omega, 08034, Barcelona, Spain

    Miquel Grau-Sánchez

  2. Department of Mathematics, Technical University of Catalonia ⋅ BarcelonaTech, Edifici TR5 (ESEIAAT), 08222, Terrassa, Spain

    Miquel Noguera

Authors
  1. Miquel Grau-Sánchez
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  2. Miquel Noguera
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Correspondence to Miquel Grau-Sánchez .

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Editors and Affiliations

  1. Departamento de Matemática, Aplicada y Estadística Universidad Politécnica de Cartagena, Cartagena, Spain

    Sergio Amat

  2. Departamento de Matemática, Aplicada y Estadística Universidad Politécnica de Cartagena, Cartagena, Spain

    Sonia Busquier

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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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