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pro vyhledávání: '"Plato, Robert"'
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 model that the searched-for solution of the considered nonlinear operato
Externí odkaz:
http://arxiv.org/abs/2305.00232
Numerical differentiation of a function, contaminated with noise, over the unit interval $[0,1] \subset \mathbb{R}$ by inverting the simple integration operator $J:L^2([0,1]) \to L^2([0,1])$ defined as $[Jx](s):=\int_0^s x(t) dt$ is discussed extensi
Externí odkaz:
http://arxiv.org/abs/2303.14473
Autor:
Klinkhammer, Chantal, Plato, Robert
We study the application of Tikhonov regularization to ill-posed nonlinear operator equations. The objective of this work is to prove low order convergence rates for the discrepancy principle under low order source conditions of logarithmic type. We
Externí odkaz:
http://arxiv.org/abs/2212.13366
Autor:
Plato, Robert, Hofmann, Bernd
In the present work, we discuss variational regularization for ill-posed nonlinear problems with focus on an oversmoothing penalty term. This means in our model that the searched-for solution of the considered nonlinear operator equation does not bel
Externí odkaz:
http://arxiv.org/abs/2206.02010
The analysis of Tikhonov regularization for nonlinear ill-posed equations with smoothness promoting penalties is an important topic in inverse problem theory. With focus on Hilbert scale models, the case of oversmoothing penalties, i.e., when the pen
Externí odkaz:
http://arxiv.org/abs/2012.11216
Autor:
Hofmann, Bernd, Plato, Robert
For the Tikhonov regularization of ill-posed nonlinear operator equations, convergence is studied in a Hilbert scale setting. We include the case of oversmoothing penalty terms, which means that the exact solution does not belong to the domain of def
Externí odkaz:
http://arxiv.org/abs/1911.00669
There are various ways to regularize ill-posed operator equations in Hilbert space. If the underlying operator is accretive then Lavrentiev regularization (singular perturbation) is an immediate choice. The corresponding convergence rates for the reg
Autor:
Plato, Robert, Hofmann, Bernd
We consider perturbed nonlinear ill-posed equations in Hilbert spaces, with operators that are monotone on a given closed convex subset. A simple stable approach is Lavrentiev regularization, but existence of solutions of the regularized equation on
Externí odkaz:
http://arxiv.org/abs/1806.00743
Autor:
Plato, Robert
In the present paper we consider the regularizing properties of the repeated midpoint rule for the stable solution of weakly singular Volterra integral equations of the first kind with perturbed right hand sides. The H\"older continuity of the soluti
Externí odkaz:
http://arxiv.org/abs/1709.03142