Local convergence of the Gauss–Newton method for injective-overdetermined systems of equations under a majorant condition

A local convergence analysis of the Gauss–Newton method for solving injective-overdetermined systems of nonlinear equations under a majorant condition is provided. The convergence as well as results on its rate are established without a convexity hypothesis on the derivative of the majorant function. The optimal convergence radius, the biggest range for uniqueness of the solution along with some other special cases are also obtained.