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    STUDIA MATHEMATICA - Issue no. 4 / 2017  
         
  Article:   EXTENDED LOCAL CONVERGENCE ANALYSIS OF INEXACT GAUSS-NEWTON METHOD FOR SINGULAR SYSTEMS OF EQUATIONS UNDER WEAK CONDITIONS.

Authors:  IOANNIS K. ARGYROS, SANTHOSH GEORGE.
 
       
         
  Abstract:  
DOI: 10.24193/subbmath.2017.4.11

Published Online: 2017-12-03
Published Print: 2017-12-03
pp. 543-558

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A new local convergence analysis of the Gauss-Newton method for solving some optimization problems is presented using restricted convergence domains. The results extend the applicability of the Gauss-Newton method under the same computational cost given in earlier studies. In particular, the advantages are: the error estimates on the distances involved are tighter and the convergence ball is at least as large. Moreover, the majorant function in contrast to earlier studies is not necessarily dierentiable. Numerical examples are also provided in this study.

Mathematics Subject Classification (2010): 65D10, 65D99, 65G99, 65K10, 90C30.

Keywords: Gauss-Newton method, local convergence, restricted convergence domains, majorant function, center-majorant function, convergence ball.
 
         
     
         
         
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