Open Access
December 2010 On the Degree of Ill-posedness for Linear Problems with Noncompact Operators
Bernd Hofmann, Stefan Kindermann
Methods Appl. Anal. 17(4): 445-462 (December 2010).


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.


Download Citation

Bernd Hofmann. Stefan Kindermann. "On the Degree of Ill-posedness for Linear Problems with Noncompact Operators." Methods Appl. Anal. 17 (4) 445 - 462, December 2010.


Published: December 2010
First available in Project Euclid: 24 May 2011

zbMATH: 1228.47017
MathSciNet: MR2800562

Primary: 47A52 , 65J20

Keywords: degree of ill-posedness , Hilbert space , linear operator equation , modulus of continuity , regularization , source condition , Spectral distribution

Rights: Copyright © 2010 International Press of Boston

Vol.17 • No. 4 • December 2010
Back to Top