Methods and Applications of Analysis
- Methods Appl. Anal.
- Volume 17, Number 4 (2010), 445-462.
On the Degree of Ill-posedness for Linear Problems with Noncompact Operators
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.
Methods Appl. Anal., Volume 17, Number 4 (2010), 445-462.
First available in Project Euclid: 24 May 2011
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Hofmann, Bernd; Kindermann, Stefan. On the Degree of Ill-posedness for Linear Problems with Noncompact Operators. Methods Appl. Anal. 17 (2010), no. 4, 445--462. https://projecteuclid.org/euclid.maa/1306249562