2 citations · 2 across the 9 of their papers we have counts for
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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…
A unified concept of the degree of ill-posedness for compact and non-compact linear operator equations in Hilbert spaces under the auspices of the spectral theorem
Frank Werner, Bernd Hofmann
Covering ill-posed problems with compact and non-compact operators regarding the degree of ill-posedness is a never ending story written by many authors in the inverse problems lit…
The degree of ill-posedness for some composition governed by the Cesaro operator
Yu Deng, Hans-Jürgen Fischer, Bernd Hofmann
In this article, we consider the singular value asymptotics of compositions of compact linear operators mapping in the real Hilbert space of quadratically integrable functions over…
Curious ill-posedness phenomena in the composition of non-compact linear operators in Hilbert spaces
Stefan Kindermann, Bernd Hofmann
We consider the composition of operators with non-closed range in Hilbert spaces and how the nature of ill-posedness is affected by their composition. Specifically, we study the \m…
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…