37 citations · 59 across the 12 of their papers we have counts for
14 papers
Randomized sketching for Krylov approximations of large-scale matrix functions
Stefan Güttel, Marcel Schweitzer
The computation of f(A)b, the action of a matrix function on a vector, is a task arising in many areas of scientific computing. In many applications, the matrix A is sparse but so…
Closing the Performance Gap with Modern C++
Thomas Heller, Hartmut Kaiser, Patrick Diehl +2
On the way to Exascale, programmers face the increasing challenge of having to support multiple hardware architectures from the same code base. At the same time, portability of cod…
Krylov subspace restarting for matrix Laplace transforms
Andreas Frommer, Karsten Kahl, Marcel Schweitzer +1
A common way to approximate -- the action of a matrix function on a vector -- is to use the Arnoldi approximation. Since a new vector needs to be generated and stored in ev…
Integral representations for higher-order Fréchet derivatives of matrix functions: Quadrature algorithms and new results on the level-2 condition number
Marcel Schweitzer
We propose an integral representation for the higher-order Fréchet derivative of analytic matrix functions which unifies known results for the first-order Fréchet derivative…
Decay bounds for Bernstein functions of Hermitian matrices with applications to the fractional graph Laplacian
Marcel Schweitzer
For many functions of matrices , it is known that their entries exhibit a rapid -- often exponential or even superexponential -- decay away from the sparsity pattern of the m…
A dimension-oblivious domain decomposition method based on space-filling curves
Michael Griebel, Marc Alexander Schweitzer, Lukas Troska
In this paper we present an algebraic dimension-oblivious two-level domain decomposition solver for discretizations of elliptic partial differential equations. The proposed paralle…
A Fracture Multiscale Model for Peridynamic enrichment within the Partition of Unity Method
Matthias Birner, Patrick Diehl, Robert Lipton +1
Partition of unity methods (PUM) are of domain decomposition type and provide the opportunity for multiscale and multiphysics numerical modeling. Different physical models can exis…
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…
Orbital-enriched Flat-top Partition of Unity Method for the Schrödinger Eigenproblem
Clelia Albrecht, Constanze Klaar, John E. Pask +3
Quantum mechanical calculations require the repeated solution of a Schrödinger equation for the wavefunctions of the system. Recent work has shown that enriched finite element meth…
Low-rank updates of matrix functions
Bernhard Beckermann, Daniel Kressner, Marcel Schweitzer
We consider the task of updating a matrix function when the matrix is subject to a low-rank modification. In other words, we aim at approximat…