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1	Ill-Posedness Aspects of Some Nonlinear Inverse Problems and their Linearizations Fleischer, G., Hofmann, B. 30 October 1998 (has links) (PDF) In this paper we deal with aspects of characterizing the ill-posedn ess of nonlinear inverse problems based on the discussion of specific examples. In particular, a parameter identification problem to a second order differential equation and its ill-posed linear components are under consideration. A new approach to the classification ofill-posedness degrees for multiplication operators completes the paper. degree of ill-posedness multiplication op erators nonlinear inverse problems parameter identification MSC 65J20 MSC 47B38 ddc:510
2	Ill-Posedness Aspects of Some Nonlinear Inverse Problems and their Linearizations Fleischer, G., Hofmann, B. 30 October 1998 (has links) In this paper we deal with aspects of characterizing the ill-posedn ess of nonlinear inverse problems based on the discussion of specific examples. In particular, a parameter identification problem to a second order differential equation and its ill-posed linear components are under consideration. A new approach to the classification ofill-posedness degrees for multiplication operators completes the paper. info:eu-repo/classification/ddc/510 ddc:510 degree of ill-posedness multiplication op erators nonlinear inverse problems parameter identification MSC 65J20 MSC 47B38
3	On Ill-Posedness and Local Ill-Posedness of Operator Equations in Hilbert Spaces Hofmann, B. 30 October 1998 (has links) (PDF) In this paper, we study ill-posedness concepts of nonlinear and linear inverse problems in a Hilbert space setting. We define local ill-posedness of a nonlinear operator equation $F(x) = y_0$ in a solution point $x_0$ and the interplay between the nonlinear problem and its linearization using the Frechet derivative $F\acent(x_0)$ . To find an appropriate ill-posedness concept for the linarized equation we define intrinsic ill-posedness for linear operator equations $Ax = y$ and compare this approach with the ill-posedness definitions due to Hadamard and Nashed. Nonlinear inverse problems oerator equations ill-posedness stability estimates local ill-posedness Frechet derivative linearized problem compact operators integral equations parameter identification MSC 65J20 MSC 47H15 MSC 65J10 MSC 65J15 MSC 65R30 MSC 45G10 ddc:510
4	On Ill-Posedness and Local Ill-Posedness of Operator Equations in Hilbert Spaces: On Ill-Posedness and Local Ill-Posedness of OperatorEquations in Hilbert Spaces Hofmann, B. 30 October 1998 (has links) In this paper, we study ill-posedness concepts of nonlinear and linear inverse problems in a Hilbert space setting. We define local ill-posedness of a nonlinear operator equation $F(x) = y_0$ in a solution point $x_0$ and the interplay between the nonlinear problem and its linearization using the Frechet derivative $F\acent(x_0)$ . To find an appropriate ill-posedness concept for the linarized equation we define intrinsic ill-posedness for linear operator equations $Ax = y$ and compare this approach with the ill-posedness definitions due to Hadamard and Nashed. info:eu-repo/classification/ddc/510 ddc:510 Nonlinear inverse problems oerator equations ill-posedness stability estimates local ill-posedness Frechet derivative linearized problem compact operators integral equations parameter identification MSC 65J20 MSC 47H15 MSC 65J10 MSC 65J15 MSC 65R30 MSC 45G10

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