Errors of regularisation under range inclusions using variable Hilbert scales

Details Errors of regularisation under range inclusions using variable Hilbert scales Errors of regularisation under range inclusions using variable Hilbert scales

2010-05-21

arxiv.org/abs/1005.3883v1

Mathematics

Numerical Analysis

27 pages

Scientific paper

Based on the variable Hilbert scale interpolation inequality bounds for the error of regularisation methods are derived under range inclusions. In this context, new formulae for the modulus of continuity of the inverse of bounded operators with non-closed range are given. Even if one can show the equivalence of this approach to the version used previously in the literature, the new formulae and corresponding conditions are simpler than the former ones. Several examples from image processing and spectral enhancement illustrate how the new error bounds can be applied.

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