A Second Degree Method for Nonlinear Inverse Problems

Abstract

The paper is concerned with the solution of nonlinear ill-posed problems by methods that utilize the second derivative. A general predictor-corrector approach is developed; one which avoids solving quadratic equations during the iteration process. Combining regularization of each iteration step with an adequate stopping condition leads to a general regularization scheme for nonlinear equations. Possible implementations and discussion of the performance of this method are illustrated by applications to some well-known inverse problems.