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


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Article Info

DATE

2014-10-07

AUTHORS

Ioannis K. Argyros, Á. Alberto 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. More... »

PAGES

423-439

References to SciGraph publications

  • 1986-01. A Kantorovich-type convergence analysis for the Gauss-Newton-Method in NUMERISCHE MATHEMATIK
  • 2009-04-22. Local convergence analysis of inexact Newton-like methods under majorant condition in COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
  • 2011-02-01. Extending the applicability of the Gauss–Newton method under average Lipschitz–type conditions in NUMERICAL ALGORITHMS
  • 2007-10-26. The convergence analysis of inexact Gauss–Newton methods for nonlinear problems in COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
  • 1986. Newton’s Method Estimates from Data at One Point in THE MERGING OF DISCIPLINES: NEW DIRECTIONS IN PURE, APPLIED, AND COMPUTATIONAL MATHEMATICS
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    http://dx.doi.org/10.1007/s10589-014-9704-6

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