Local convergence analysis of inexact Gauss-Newton like methods under majorant condition

摘要

In this paper, we present a local convergence analysis of inexactGauss-Newton like methods for solving nonlinear least squares problems. Underthe hypothesis that the derivative of the function associated with the leastsquare problem satisfies a majorant condition, we obtain that the method iswell-defined and converges. Our analysis provides a clear relationship betweenthe majorant function and the function associated with the least squareproblem. It also allows us to obtain an estimate of convergence ball forinexact Gauss-Newton like methods and some important, special cases.