5 papers
A fault-tolerant domain decomposition method based on space-filling curves
Michael Griebel, Marc-Alexander Schweitzer, Lukas Troska
We propose a simple domain decomposition method for -dimensional elliptic PDEs which involves an overlapping decomposition into local subdomain problems and a global coarse prob…
Analysis of probing techniques for sparse approximation and trace estimation of decaying matrix functions
Andreas Frommer, Claudia Schimmel, Marcel Schweitzer
The computation of matrix functions , or related quantities like their trace, is an important but challenging task, in particular for large and sparse matrices . In recent…
Computing low-rank approximations of the Fréchet derivative of a matrix function using Krylov subspace methods
Peter Kandolf, Antti Koskela, Samuel D. Relton +1
The Fréchet derivative of the matrix function plays an important role in many different applications, including condition number estimation and network analysis.…
Low-rank updates of matrix functions II: Rational Krylov methods
Bernhard Beckermann, Alice Cortinovis, Daniel Kressner +1
This work develops novel rational Krylov methods for updating a large-scale matrix function f(A) when A is subject to low-rank modifications. It extends our previous work in this c…
A comparison of limited-memory Krylov methods for Stieltjes functions of Hermitian matrices
Stefan Güttel, Marcel Schweitzer
Given a limited amount of memory and a target accuracy, we propose and compare several polynomial Krylov methods for the approximation of f(A)b, the action of a Stieltjes matrix fu…