Regularization of exponentially ill-posed problems

By Thorsten Hohage. 2000

181 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Computational Mechanics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f7b3428e0919cee4e0bad6d96544ed561de537be

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In Biomedical Engineering

In Computational Mechanics

In Mathematical Physics

Citations in the corpus

Morozov's Discrepancy Principle under General Source Conditions (2003, methodology): “For the general regularization of form (3.1), Hohage [5] proved a result analogous to Corollary 3.5 under the assumption on gα that λµ[1 − λgα(λ)] ≤ cµαµ for 0 ≤ µ ≤ µ0 for some µ0 > 0.”
Fourier regularization method for solving a Cauchy problem for the Laplace equation (2008, background): “Hohage in [20], and due to the results given in [20] we also know that estimate (2.”
Geometry of linear ill-posed problems in variable Hilbert scales Inverse Problems 19 789-803 (2003, background): “This class covers all source conditions, studied do far, in particular by Hohage [8].”
Convergence rates for Tikhonov regularization from different kinds of smoothness conditions (2006, background): “For such logarithmic rates, converse results were established in [15]: if ‖xα − x†‖ = O ((− lnα)−p) as α → 0, then for each 0 < q < p there exists a uq ∈ X such that x† = (− ln (A∗A))−q uq.”
An extension of the variational inequality approach for obtaining convergence rates in regularization of nonlinear ill-posed problems (2010, background): “This includes the case of logarithmic convergence rates (see the papers [17, 18] by Hohage and Kaltenbacher).”
Lavrentiev Regularization for Linear Ill-Posed Problems under General Source Conditions (2004, unknown): “2) has to be understood in the sense x = φ(A)v with φ(λ) = [ ln 1 λ ]−p, (see [10, 15, 22, 27]).”
Approximate source conditions in Tikhonov–Phillips regularization and consequences for inverse problems with multiplication operators (2006, background): “Nevertheless, the convergence rate (22) implies for the choice (21) also the order optimal rate (17) as already mentioned in [22] and [29].”