13 citations · 13 across the 1 of their papers we have counts for
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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…
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…
New results for variational regularization with oversmoothing penalty term in Banach spaces
Bernd Hofmann, Chantal Klinkhammer, Robert Plato
In this article on variational regularization for ill-posed nonlinear problems, we are once again discussing the consequences of an oversmoothing penalty term. This means in our mo…
A note on the degree of ill-posedness for mixed differentiation on the d-dimensional unit cube
Bernd Hofmann, Hans-Jürgen Fischer, Robert Plato
Numerical differentiation of a function, contaminated with noise, over the unit interval by inverting the simple integration operator $J:L^2([0,1]) \to L…