Extended local convergence analysis of inexact Gauss-Newton method for singular systems of equations under weak conditions

Abstract

Abstract.A new local convergence analysis of the Gauss-Newton method for solving some optimization problems is presented using restricted convergence domains. The results extend the applicability of the Gauss-Newton method under the same computational cost given in earlier studies. In particular, the advantages are: the error estimates on the distances involved are tighter and the convergence ball is at least as large. Moreover, the majorant function in contrast to earlier studies is not necessarily differentiable. Numerical examples are also provided in this study.Mathematics Subject Classification (2010): 65D10, 65D99, 65G99, 65K10, 90C30.

Ball Convergence of an Efficient Eighth Order Iterative Method Under Weak Conditions

“…Consequently, we study the local convergence of Method (2) using hypotheses on the first Fréchet-derivative only by taking advantage of the Lipschitz continuity of the first Fréchet-derivative. There exist many studies which deal with the local and semilocal convergence of iterative methods (see, for example, [2,[4][5][6][7][8][9][10][11][12][13][14][15][16]). In particular, relevant work can be found in [17] for the special case…”