Hettlich, F.; Rundell, W. A second degree method for nonlinear inverse problems. (English) Zbl 0946.35115 SIAM J. Numer. Anal. 37, No. 2, 587-620 (2000). Summary: 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. Cited in 2 ReviewsCited in 30 Documents MSC: 35R30 Inverse problems for PDEs 65J15 Numerical solutions to equations with nonlinear operators 65J20 Numerical solutions of ill-posed problems in abstract spaces; regularization Keywords:nonlinear ill-posed problems; iterative regularization methods; domain derivative PDFBibTeX XMLCite \textit{F. Hettlich} and \textit{W. Rundell}, SIAM J. Numer. Anal. 37, No. 2, 587--620 (2000; Zbl 0946.35115) Full Text: DOI