Interpolation in variable Hilbert scales with application to inverse problems
- Mathé, Peter
- Tautenhahn, Ulrich
2010 Mathematics Subject Classification
- 65J20 46B70 65R30
- Regularization, interpolation spaces, Hilbert scales
For solving linear ill-posed problems with noisy data regularization methods are required. In the present paper regularized approximations in Hilbert scales are obtained by a general regularization scheme. The analysis of such schemes is based on new results for interpolation in Hilbert scales. Error bounds are obtained under general smoothness conditions.
- Inverse Problems, 22 (2006) pp. 2271--2297.