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

Ioannis Argyros () and Á. Magreñán ()

Computational Optimization and Applications, 2015, vol. 60, issue 2, 423-439

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

Keywords: Least squares problems; Newton–Gauss methods; Banach space; Majorant condition; Local convergence; 90C30; 65G99; 65K10; 47H17; 49M15 (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s10589-014-9704-6

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