EXPANDING THE APPLICABILITY OF THE GAUSS-NEWTON METHOD FOR A CERTAIN CLASS OF SYSTEMS OF EQUATIONS

Abstract

We 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.