4 papers · 1 filter
Regularization of the metric generalized inverse in Banach spaces and the dichotomy phenomenon
Peter Mathé, Bernd Hofmann
For a bounded linear operator acting between Banach spaces, its metric generalized inverse is the analog to the prominent Moore-Penrose inverse for operators acting between Hilbert…
Interpolation and inverse problems in spectral Barron spaces
Shuai Lu, Peter Mathé
Spectral Barron spaces, which quantify the absolute value of weighted Fourier coefficients of a function, have gained considerable attention due to their capability for universal a…
Comparing the ill-posedness for linear operators in Hilbert spaces
Peter Mathé, Bernd Hofmann
The difficulty for solving ill-posed linear operator equations in Hilbert space is reflected by the strength of ill-posedness of the governing operator, and the inherent solution s…
Tractability of linear ill-posed problems in Hilbert space
Peter Mathé, Bernd Hofmann
We introduce a notion of tractability for ill-posed operator equations in Hilbert space. For such operator equations the asymptotics of the best possible rate of reconstruction in…