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Improved local convergence analysis of the Gauss–Newton method under a majorant condition

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  • Ioannis Argyros
  • Á. Magreñán

Abstract

We present a local convergence analysis of Gauss-Newton method for solving nonlinear least square problems. Using more precise majorant conditions than in earlier studies such as Chen (Comput Optim Appl 40:97–118, 2008 ), Chen and Li (Appl Math Comput 170:686–705, 2005 ), Chen and Li (Appl Math Comput 324:1381–1394, 2006 ), Ferreira (J Comput Appl Math 235:1515–1522, 2011 ), Ferreira and Gonçalves (Comput Optim Appl 48:1–21, 2011 ), Ferreira and Gonçalves (J Complex 27(1):111–125, 2011 ), Li et al. (J Complex 26:268–295, 2010 ), Li et al. (Comput Optim Appl 47:1057–1067, 2004 ), Proinov (J Complex 25:38–62, 2009 ), Ewing, Gross, Martin (eds.) (The merging of disciplines: new directions in pure, applied and computational mathematics 185–196, 1986 ), Traup (Iterative methods for the solution of equations, 1964 ), Wang (J Numer Anal 20:123–134, 2000 ), we provide a larger radius of convergence; tighter error estimates on the distances involved and a clearer relationship between the majorant function and the associated least squares problem. Moreover, these advantages are obtained under the same computational cost. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Ioannis Argyros & Á. Magreñán, 2015. "Improved local convergence analysis of the Gauss–Newton method under a majorant condition," Computational Optimization and Applications, Springer, vol. 60(2), pages 423-439, March.
    • Handle: RePEc:spr:coopap:v:60:y:2015:i:2:p:423-439
    DOI: 10.1007/s10589-014-9704-6
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    References listed on IDEAS

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    1. O. Ferreira & M. Gonçalves, 2011. "Local convergence analysis of inexact Newton-like methods under majorant condition," Computational Optimization and Applications, Springer, vol. 48(1), pages 1-21, January.
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