2 citations · 2 across the 9 of their papers we have counts for
10 papers
Duality of uncomplemented null-space and non-closed range and its impact on the regularization of Mazur-type operators
Jens Flemming, Bernd Hofmann
Up to now operators with uncomplemented null-space have been playing only a minor role in regularization theory for ill-posed inverse problems in Banach spaces. We show that ill-po…
A note on the Goldberg-Thorp example in light of the classification of linear ill-posed problems in Banach spaces
Bernd Hofmann, Jens Flemming
This note considers the strictly singular mapping, denoted by , from onto of an example by Goldberg and Thorp from 1963 as a typical hybrid-type operator in th…
New aspects of ill-posedness classification in Banach spaces
Jens Flemming, Bernd Hofmann
Motivated by a seminal paper of professor M. Z. Nashed published in 1987 on classification of ill-posed linear operator equations and distinguishing two types of ill-posedness in B…
Classification of ill-posedness for bounded linear operators in Banach spaces
Bernd Hofmann, Stefan Kindermann
In this article, concepts of well- and ill-posedness for linear operators in Hilbert and Banach spaces are discussed. While these concepts are well understood in Hilbert spaces, th…
Operator ordering by ill-posedness in Hilbert and Banach spaces
Stefan Kindermann, Bernd Hofmann
For operators representing ill-posed problems, an ordering by ill-posedness is proposed, where one operator is considered more ill-posed than another one if the former can be expre…
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…