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

نویسنده

  • Bernd Hofmann
چکیده

In this paper, we study ill-posedness concepts of nonlinear and linear inverse problems in a Hilbert space setting. We deene 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 Fr echet derivative F 0 (x 0). To nd an appropriate ill-posedness concept for 1 the linearized equation we deene intrinsic ill-posedness for linear operator equations Ax = y and compare this approach with the ill-posedness deenitions due to Hadamard and Nashed.

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تاریخ انتشار 1997