T. Gergelits

collaborators

3 papers

math.NA2021

Mixed Precision $s$ -step Lanczos and Conjugate Gradient Algorithms

Erin Carson, Tomáš Gergelits

Compared to the classical Lanczos algorithm, the $s$ -step Lanczos variant has the potential to improve performance by asymptotically decreasing the synchronization cost per iterati…

math.NA2021

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,…

math.AP2020

Generalized spectrum of second order differential operators

Tomáš Gergelits, Bjørn Fredrik Nielsen, Zdeněk Strakoš

We analyze the spectrum of the operator $Δ^{- 1} [\nabla \cdot (K \nabla u)]$ , where $Δ$ denotes the Laplacian and $K = K (x, y)$ is a symmetric tensor. Our main result shows that this s…

Mixed Precision s-step Lanczos and Conjugate Gradient Algorithms

Numerical approximation of the spectrum of self-adjoint continuously invertible operators

Generalized spectrum of second order differential operators

Mixed Precision $s$ -step Lanczos and Conjugate Gradient Algorithms