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Higher-Order Method for the Solution of a Nonlinear Scalar Equation

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Abstract

A new iterative method to find the root of a nonlinear scalar function f is proposed. The method is based on a suitable Taylor polynomial model of order n around the current point x k and involves at each iteration the solution of a linear system of dimension n. It is shown that the coefficient matrix of the linear system is nonsingular if and only if the first derivative of f at x k is not null. Moreover, it is proved that the method is locally convergent with order of convergence at least n + 1. Finally, an easily implementable scheme is provided and some numerical results are reported.

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Authors and Affiliations

  1. Department of Electrical Engineering, University of L’Aquila, L’Aquila, Italy

    A. Germani (Professor, Researcher) & C. Manes (Associate Professor, Researcher)

  2. Istituto di Analisi dei Sistemi ed Informatica A. Ruberti, CNR, Rome, Italy

    A. Germani (Professor, Researcher), C. Manes (Associate Professor, Researcher), P. Palumbo (Researcher) & M. Sciandrone (Researcher)

Authors
  1. A. Germani
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  2. C. Manes
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  3. P. Palumbo
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  4. M. Sciandrone
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Corresponding author

Correspondence to M. Sciandrone.

Additional information

Communicated by F. A. Potra

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Germani, A., Manes, C., Palumbo, P. et al. Higher-Order Method for the Solution of a Nonlinear Scalar Equation. J Optim Theory Appl 131, 347–364 (2006). https://doi.org/10.1007/s10957-006-9154-0

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  • DOI: https://doi.org/10.1007/s10957-006-9154-0

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