Expanding the applicability of the Gauss-Newton method for a certain class of systems of equations


  • Ioannis K. Argyros Cameron University, USA
  • Santhosh George National Institute of Technology Karnataka, India




Gauss-Newton method, Newton method, semilocal convergence, least squares problem
Abstract views: 204


We present a new semilocal convergence analysis of the Gauss-Newton method in order to solve a certain class of systems of equations under a majorant condition. Using a center majorant function as well as a majorant function and under the same computational cost as in earlier studies such as [11]-[13], we present a semilocal convergence analysis with the following advantages: weaker sufficient convergence conditions; tighter error estimates on the distances involved and an at least as precise information on the location of the solution. Special cases and applications complete this study.


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Author Biography

Ioannis K. Argyros, Cameron University, USA

Full tenured Professor of Mathematics.


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How to Cite

Argyros, I. K., & George, S. (2016). Expanding the applicability of the Gauss-Newton method for a certain class of systems of equations. J. Numer. Anal. Approx. Theory, 45(1), 3–13. https://doi.org/10.33993/jnaat451-1102