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1	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
2	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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On Ill-Posedness and Local Ill-Posedness of Operator Equations in Hilbert Spaces

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