Argyros, I.K.George, S.2026-02-052016Journal of Numerical Analysis and Approximation Theory, 2016, 45, 1, pp. 3-1324576794https://doi.org/10.33993/jnaat451-1102https://idr.nitk.ac.in/handle/123456789/25896We present a new semi-local 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 advan-tages: 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. © 2016, Publishing House of the Romanian Academy. All rights reserved.Gauss-Newton methodleast squares problemNewton’s methodsemilocal convergence