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A derivative free iterative method for solving least squares problems

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Abstract

A derivative free iterative method for approximating a solution of nonlinear least squares problems is studied first in Shakhno and Gnatyshyn (Appl Math Comput 161:253–264, 2005). The radius of convergence is determined as well as usable error estimates. We show that this method is faster than its Secant analogue examined in Shakhno and Gnatyshyn (Appl Math Comput 161:253–264, 2005). Numerical example is also provided in this paper.

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Authors and Affiliations

  1. Department of Information and Electronics, Hangzhou Radio and TV University, Hangzhou, 310012, Zhejiang, People’s Republic of China

    Hongmin Ren

  2. Department of Mathematics Sciences, Cameron University, Lawton, OK, 73505, USA

    Ioannis K. Argyros

  3. Laboratoire de Mathématiques et Applications, Poitiers University, Bd. Pierre et Marie Curie, Téléport 2, B.P. 30179, 86962, Futuroscope Chasseneuil Cedex, France

    Saïd Hilout

Authors
  1. Hongmin Ren
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  2. Ioannis K. Argyros
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  3. Saïd Hilout
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Correspondence to Ioannis K. Argyros.

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Ren, H., Argyros, I.K. & Hilout, S. A derivative free iterative method for solving least squares problems. Numer Algor 58, 555–571 (2011). https://doi.org/10.1007/s11075-011-9470-9

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  • DOI: https://doi.org/10.1007/s11075-011-9470-9

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