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

Ioannis K. Argyros; Santhosh George

doi:10.33993/jnaat451-1102

Authors

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

DOI:

https://doi.org/10.33993/jnaat451-1102

Keywords:

Gauss-Newton method, Newton method, semilocal convergence, least squares problem

Abstract views: 239

Abstract

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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