On an operator equation with noise in the operator and the right-hand side with application to an inverse vibration problem
- Bruckner, Gottfried
- Yamamoto, Masahiro
2010 Mathematics Subject Classification
- 65J20 35R30 35L05
- regularization, linear operator equation, uncertain operator, noisy right-hand side, wave equation, point source reconstruction
We consider a linear operator equation with noise in the operator and the right-hand side. As a concept, the ill-posedness of the problem is composed of the ill-posedness with respect to the operator and the ill-posedness with respect to the right-hand side, and in both the cases the ill-posedness can be characterized by an embedding operator. Starting at a numerical procedure for exact data, in the case of noisy data a numerical procedure and error estimates are given. As an example, a Volterra integral equation of the first kind is investigated and finally applied to a point source reconstruction problem for the wave equation.
- ZAMM 80, (2000), pp. 377-388