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pro vyhledávání: '"Gerth, Daniel"'
Autor:
Gerth, Daniel, Hofmann, Bernd
Publikováno v:
EURASIAN JOURNAL OF MATHEMATICAL AND COMPUTER APPLICATIONS 10(1), pp. 40--0, 2022
We address facts and open questions concerning the degree of ill-posedness of the composite Hausdorff moment problem aimed at the recovery of a function $x \in L^2(0,1)$ from elements of the infinite dimensional sequence space $\ell^2$ that character
Externí odkaz:
http://arxiv.org/abs/2206.04127
Autor:
Gerth, Daniel
Linear non-compact operators are difficult to study because they do not exist in the finite dimensional world. Recently, Math\'{e} and Hofmann studied the singular values of the compact composition of the non-compact Hausdorff moment operator and the
Externí odkaz:
http://arxiv.org/abs/2201.13185
Autor:
Koch, Josef, Classen, Silke, Gerth, Daniel, Dallmann, Natalie, Strauss, Tido, Vaugeois, Maxime, Galic, Nika
Publikováno v:
In Ecotoxicology and Environmental Safety 1 June 2024 277
Publikováno v:
In Geoderma March 2024 443
The Hausdorf moment problem (HMP) over the unit interval in an $L^2$-setting is a classical example of an ill-posed inverse problem. Since various applications can be rewritten in terms of the HMP, it has gathered significant attention in the literat
Externí odkaz:
http://arxiv.org/abs/2104.06029
Autor:
Gerth, Daniel
Tikhonov regularization with square-norm penalty for linear forward operators has been studied extensively in the literature. However, the results on convergence theory are based on technical proofs and difficult to interpret. It is also often not cl
Externí odkaz:
http://arxiv.org/abs/2103.08218
Autor:
Gerth, Daniel, Ramlau, Ronny
A main drawback of classical Tikhonov regularization is that often the parameters required to apply theoretical results, e.g., the smoothness of the sought-after solution and the noise level, are unknown in practice. In this paper we investigate in n
Externí odkaz:
http://arxiv.org/abs/2012.14875
Fibre Bragg Gratings have become widespread measurement devices in engineering and other fields of application. In all but a few cases, the relation between cause and effect is simplified to a proportional model. However, at its mathematical core lie
Externí odkaz:
http://arxiv.org/abs/2009.06509
Conditional stability estimates are a popular tool for the regularization of ill-posed problems. A drawback in particular under nonlinear operators is that additional regularization is needed for obtaining stable approximate solutions if the validity
Externí odkaz:
http://arxiv.org/abs/1905.11682
Autor:
Gerth, Daniel, Kindermann, Stefan
We show that a Kurdyka-\L{}ojasiewicz (KL) inequality can be used as regularity condition for Tikhonov regularization with linear operators in Banach spaces. In fact, we prove the equivalence of a KL inequality and various known regularity conditions
Externí odkaz:
http://arxiv.org/abs/1905.10177