On the regularization of the ill-posed logarithmic kernel integral equation of the first kind.
Authors
- Bruckner, Gottfried
2010 Mathematics Subject Classification
- 65R30 65T05 65T10
Keywords
- decomposition, ill-posed logarithmic kernel integral equations, ill-posed problem, singular value decomposition, parameter choice, regularization method, optimal convergence
DOI
Abstract
The logarithmic kernel integral equation of the first kind is investigated as improperly posed problem considering its right-hand side as observed quantity in a suitable space with a weaker norm. The improperly posed problem is decomposed into a well-posed one, extensively studied in the literature (cf. e.g. [11], [13], [14]), and an ill-posed imbedding problem. For the ill-posed part a modified truncated singular value decomposition regularization method is proposed that allows an easily performable a-posteriori parameter choice. The whole problem is then solved by combining the regularization method with a numerical procedure from [13] for the well-posed part. Finally, an error estimate is given revealing the influence of the observation error on the approximation error of the numerical procedure. For a specification of the discretization parameter as a known function of the noise level only, the optimal convergence order is achieved.
Appeared in
- Inverse Problems, 11 (1995), pp. 65--77
Download Documents