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A second degree method for nonlinear inverse problems. (English) Zbl 0946.35115

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.

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
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