4 citations · 5 across the 8 of their papers we have counts for
11 papers
A note on the convergence of the eigenvalues in a subdomain to the continuous spectrum
Miroslav Bulíček, Bjørn Fredrik Nielsen, Zdeněk Strakoš
The SIGEST paper Nielsen and Strakoš (2024) characterized the spectrum of the preconditioned operator in a bounded open two-dimensional domain $Ω…
Identifying the source term in the potential equation with weighted sparsity regularization
Ole Løseth Elvetun, Bjørn Fredrik Nielsen
We explore the possibility for using boundary measurements to recover a sparse source term f(x) in the potential equation. Employing weighted sparsity regularization and standard r…
Box constraints and weighted sparsity regularization for identifying sources in elliptic PDEs
Ole Løseth Elvetun, Bjørn Fredrik Nielsen
We explore the possibility for using boundary data to identify sources in elliptic PDEs. Even though the associated forward operator has a large null space, it turns out that box c…
Numerical approximation of the spectrum of self-adjoint continuously invertible operators
Tomáš Gergelits, Bjørn Fredrik Nielsen, Zdeněk Strakoš
This paper deals with the generalized spectrum of continuously invertible linear operators defined on infinite dimensional Hilbert spaces. More precisely, we consider two bounded,…
Weighted sparsity regularization for source identification for elliptic PDEs
Ole Løseth Elvetun, Bjørn Fredrik Nielsen
This investigation is motivated by PDE-constrained optimization problems arising in connection with electrocardiograms (ECGs) and electroencephalography (EEG). Standard sparsity re…
Modified Tikhonov regularization for identifying several sources
Ole Løseth Elvetun, Bjørn Fredrik Nielsen
We study whether a modified version of Tikhonov regularization can be used to identify several local sources from Dirichlet boundary data for a prototypical elliptic PDE. This pape…
A regularization operator for source identification for elliptic PDEs
Ole Løseth Elvetun, Bjørn Fredrik Nielsen
We study a source identification problem for a prototypical elliptic PDE from Dirichlet boundary data. This problem is ill-posed, and the involved forward operator has a significan…
Generalized spectrum of second order differential operators
Tomáš Gergelits, Bjørn Fredrik Nielsen, Zdeněk Strakoš
We analyze the spectrum of the operator , where denotes the Laplacian and is a symmetric tensor. Our main result shows that this s…
Laplacian preconditioning of elliptic PDEs: Localization of the eigenvalues of the discretized operator
Tomáš Gergelits, Kent-André Mardal, Bjørn Fredrik Nielsen +1
In the paper \textit{Preconditioning by inverting the {L}aplacian; an analysis of the eigenvalues. IMA Journal of Numerical Analysis 29, 1 (2009), 24--42}, Nielsen, Hackbusch and T…
Regularization of ill-posed point neuron models
Bjørn Fredrik Nielsen
Point neuron models with a Heaviside firing rate function can be ill-posed. That is, the initial-condition-to-solution map might become discontinuous in finite time. If a Lipschitz…
Robust preconditioners for PDE-constrained optimization with limited observations
Kent-André Mardal, Bjørn Fredrik Nielsen, Magne Nordaas
Regularization robust preconditioners for PDE-constrained optimization problems have been successfully developed. These methods, however, typically assume that observation data is…