On Ill-Posedness and Local Ill-Posedness of OperatorEquations in Hilbert Spaces
On Ill-Posedness and Local Ill-Posedness of OperatorEquations in Hilbert Spaces
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希尔伯特空间算子方程的病态性和局部病态性
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发表时间：
1998
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通讯作者：
B. Hofmann
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作者：
B. Hofmann
本文研究了Hilbert空间中非线性和线性反问题的不适定性概念。本文证明了非线性算子方程F（x）= y0在解点x0处的局部不适定性，以及利用Frechet导数F0（x0）的线性化与非线性问题之间的相互作用.为了给线性化方程找到一个合适的不适定性概念，我们定义了线性算子方程Ax = y的内在不适定性，并将这种方法与Hadamard和Nashed的不适定性进行了比较.
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.