A Second Degree Method for Nonlinear Inverse Problems
SIAM Journal on Numerical Analysis
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
An implicit Landweber method for nonlinear ill-posed operator equations
Journal of Computational and Applied Mathematics
| Hi-index | 0.00 |
In this work we are interested in the solution of nonlinear inverse problems of the form F(x) = y. We consider a two-stage method which is third order convergent for well-posed problems. Combining the method with Levenberg-Marquardt regularization of the linearized problems at each stage and using the discrepancy principle as a stopping criterion, we obtain a regularization method for ill-posed problems. Numerical experiments on some parameter identification and inverse acoustic scattering problems are presented to illustrate the performance of the method.