On the degree of ill-posedness for linear problems with noncompact operators. (English) Zbl 1228.47017

Authors’ abstract: In inverse problems, it is quite usual to encounter equations that are ill-posed and require regularization aimed at finding stable approximate solutions when the given data are noisy. In this paper, we discuss definitions and concepts for the degree of ill-posedness for linear operator equations in a Hilbert space setting. It is important to distinguish between a global version of such degree taking into account the smoothing properties of the forward operator only, and a local version combining that with the corresponding solution smoothness. We include the rarely discussed case of non-compact forward operators and explain why the usual notion of degree of ill-posedness cannot be used in this case.


47A52 Linear operators and ill-posed problems, regularization
65J20 Numerical solutions of ill-posed problems in abstract spaces; regularization
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