Jens Flemming

activity

20092026

ℓ^{1}

-regularization if the sparsity assumption fails

28 citations · 59 across the 10 of their papers we have counts for

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Showing 2017Show all

3 papers · 1 filter

math.NA2017

A converse result for Banach space convergence rates in Tikhonov-type convex regularization of ill-posed linear equations

Jens Flemming

We consider Tikhonov-type variational regularization of ill-posed linear operator equations in Banach spaces with general convex penalty functionals. Upper bounds for certain error…

math.NA2017

There always is a variational source condition for nonlinear problems in Banach spaces

Jens Flemming

Variational source conditions proved useful for deriving convergence rates for Tikhonov's regularization method and also for other methods. Up to now such conditions have been veri…

math.FA2017★ 1 cited

Injectivity and weak*-to-weak continuity suffice for convergence rates in $ℓ^{1}$ -regularization

Jens Flemming, Daniel Gerth

We show that the convergence rate of $ℓ^{1}$ -regularization for linear ill-posed equations is always $O (δ)$ if the exact solution is sparse and if the considered operator is injec…

A converse result for Banach space convergence rates in Tikhonov-type convex regularization of ill-posed linear equations

There always is a variational source condition for nonlinear problems in Banach spaces

Injectivity and weak*-to-weak continuity suffice for convergence rates in ℓ1-regularization

Injectivity and weak*-to-weak continuity suffice for convergence rates in $ℓ^{1}$ -regularization