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Advances in Iterative Methods for Nonlinear Equations pp 5–21Cite as

An Overview on Steffensen-Type Methods

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

Abstract

In this chapter we present an extensive overview of Steffensen-type methods. We first present the real study of the methods and then we present the complex dynamics related this type of methods applied to different polynomials. We also provide an extension to Banach space settings and an application to a Boundary Value Problem. We finish this chapter with contributions to this matter made by other authors.

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Acknowledgements

The research has been partially funded by UNIR Research (http://research.unir.net), Universidad Internacional de La Rioja (UNIR, http://www.unir.net), under the Research Support Strategy 3 [2015–2017], Research Group: MOdelación Matemática Aplicada a la INgeniería (MOMAIN), by the Grant SENECA 19374/PI/14 and by the project MTM2014-52016-C2-1-P of the Spanish Ministry of Economy and Competitiveness.

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Authors and Affiliations

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

    S. Amat & S. Busquier

  2. Escuela de Ingeniería, Universidad Internacional de La Rioja (UNIR), C/Gran Vía 41, 26005, Logroño, (La Rioja), Spain

    Á. A. Magreñán

  3. Facultad de Educación, Universidad Internacional de La Rioja (UNIR), C/Gran Vía 41, 26005, Logroño, (La Rioja), Spain

    L. Orcos

Authors
  1. S. Amat
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  2. S. Busquier
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  3. Á. A. Magreñán
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  4. L. Orcos
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Corresponding author

Correspondence to Á. A. Magreñán .

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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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Amat, S., Busquier, S., Magreñán, Á.A., Orcos, L. (2016). An Overview on Steffensen-Type Methods. 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_2

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