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Determination of multiple roots of nonlinear equations and applications

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Abstract

In this work we focus on the problem of approximating multiple roots of nonlinear equations. Multiple roots appear in some applications such as the compression of band-limited signals and the multipactor effect in electronic devices. We present a new family of iterative methods for multiple roots whose multiplicity is known. The methods are optimal in Kung–Traub’s sense (Kung and Traub in J Assoc Comput Mach 21:643–651, [1]), because only three functional values per iteration are computed. By adding just one more function evaluation we make this family derivative free while preserving the convergence order. To check the theoretical results, we codify the new algorithms and apply them to different numerical examples.

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Authors and Affiliations

  1. Instituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, Valencia, Spain

    José L. Hueso & Carles Teruel

  2. Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Valencia, Spain

    Eulalia Martínez

Authors
  1. José L. Hueso
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  2. Eulalia Martínez
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  3. Carles Teruel
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Corresponding author

Correspondence to José L. Hueso.

Additional information

This research was supported by Ministerio de Ciencia y Tecnología MTM2011-28636-C02-02 and by Vicerrectorado de Investigación, Universitat Politècnica de València PAID-SP-2012-0474.

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Hueso, J.L., Martínez, E. & Teruel, C. Determination of multiple roots of nonlinear equations and applications. J Math Chem 53, 880–892 (2015). https://doi.org/10.1007/s10910-014-0460-8

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  • DOI: https://doi.org/10.1007/s10910-014-0460-8

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