Regularizing Properties of a Truncated Newton-cg Algorithm for Nonlinear Inverse Problems

This paper develops truncated Newton methods as an appropriate tool for nonlinear inverse problems which are ill-posed in the sense of Hadamard. In each Newton step an approximate solution for the linearized problem is computed with the conjugate gradient method as an inner iteration. The conjugate gradient iteration is terminated when the residual has been reduced to a prescribed percentage. Under certain assumptions on the nonlinear operator it is shown that the algorithm converges and is stable if the discrepancy principle is used to terminate the outer iteration. These assumptions are fulllled, e.g., for the inverse problem of identifying the diiusion coeecient in a parabolic diierential equation from distributed data.