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Inexact Gauss-Newton like methods for injective-overdetermined systems of equations under a majorant condition. (English) Zbl 1343.65059
The authors consider injective-overdetermined systems of nonlinear equations, i.e., nonlinear systems of the form \(F(x)=0\), for which the derivative \(F'(x)\) is injective, as linear operator. For solving such a system they propose an inexact Gauss-Newton iteration which in its iterations replace the exact solution of linear system involving \(F'(x)\) with an iteratively computed approximation. They prove convergence of the new algorithm together with some applications.

MSC:
65H10 Numerical computation of solutions to systems of equations
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