ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

15. Numerical Analysis and Scientific Computing

1991 MS Classification: 65J20,35R30 Bruckner, Gottfried, WIAS Berlin, Germany On the regularization of an inverse vibration problem with noisy data 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 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 first kind Volterra integral equation is investigated and finally applied to a point source reconstruction problem for the wave equation.