Zhang, Gui; Huang, Sixun A Newton-type method for the regularization of nonlinear ill-posed problems. (Chinese. English summary) Zbl 1048.65057 Chin. Ann. Math., Ser. A 24, No. 3, 321-330 (2003). Summary: The authors consider a Newton-type method, for regularizing the abstract nonlinear ill-posed operator equation \(F(x)=y\). Under certain smoothness conditions on the nonlinear operator, they obtain the local convergence of the method. By further assumptions on the closeness and smoothness of the exact solution, a stopping rule to terminate the iteration is proposed and the suitable rates of convergence is derived. MSC: 65J15 Numerical solutions to equations with nonlinear operators 65J20 Numerical solutions of ill-posed problems in abstract spaces; regularization 47J06 Nonlinear ill-posed problems Keywords:regularization; nonlinear operation equations; nonlinear ill-posed problems; Newton-type method; stopping rule; convergence PDFBibTeX XMLCite \textit{G. Zhang} and \textit{S. Huang}, Chin. Ann. Math., Ser. A 24, No. 3, 321--330 (2003; Zbl 1048.65057)