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A Newton-type method for the regularization of nonlinear ill-posed problems. (Chinese. English summary) Zbl 1048.65057

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
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