Regularizing properties of a truncated Newton-cg algorithm for nonlinear inverse problems. (English) Zbl 0899.65038

Hanke, Martin

Numer. Funct. Anal. Optimization 18, No. 9-10, 971-993 (1997).

For the numerical solution of nonlinear ill-posed problems, a truncated Newton method is considered, i.e., in each Newton step an approximate solution of the corresponding linearized problem is computed with the conjugate gradient method applied to the associated normal equations. The conjugate gradient method as the inner iteration is terminated when the residual has been reduced to a given percentage. Convergence of this method is shown under certain assumptions on the nonlinear operator, and moreover, in the case of perturbed data the regularizing properties of a discrepancy principle as a stopping rule for the Newton method are analyzed.

Reviewer: Robert Plato (Berlin)

MSC:

65J15	Numerical solutions to equations with nonlinear operators (do not use 65Hxx)
65J20	Numerical solutions of ill-posed problems in abstract spaces; regularization
47J25	Iterative procedures involving nonlinear operators

Keywords:

nonlinear ill-posed problems; regularization; truncated Newton method; conjugate gradient method; convergence; discrepancy principle