4 papers
Mixed Precision -step Lanczos and Conjugate Gradient Algorithms
Erin Carson, Tomáš Gergelits
Compared to the classical Lanczos algorithm, the -step Lanczos variant has the potential to improve performance by asymptotically decreasing the synchronization cost per iterati…
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,…
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…