On the characterization of self-regularization properties of a fully discrete projection method for Symm's integral equation
- Pereverzev, Sergei V.
- Prößdorf, Siegfried
2010 Mathematics Subject Classification
- 65R30 65R20 45L10
- Symm's integral equation, ill-posed problem, fully discrete projection method, perturbations in the data, error analysis, self-regularization
The influence of small perturbations in the kernel and the right-hand side of Symm's boundary integral equation, considered in an ill-posed setting, is analyzed. We propose a modification of a fully discrete projection method which is more economical in the sense of complexity and allows to obtain the optimal order of accuracy in the power scale with respect to the level of the noise in the kernel or in the parametric representation of the boundary.