14 citations · 30 across the 9 of their papers we have counts for
6 papers · 1 filter
A GPU-Accelerated Blocked Adaptive Randomized Range Finder Based on an Implicit Householder QR Decomposition
Carolin Penke, Andreas Herten
Low-rank methods can reduce the memory and computational requirements of deep neural network training in approaches such as GaLore. Randomized range finders offer an attractive alt…
A Structure-Preserving Divide-and-Conquer Method for Pseudosymmetric Matrices
Peter Benner, Yuji Nakatsukasa, Carolin Penke
We devise a spectral divide-and-conquer scheme for matrices that are self-adjoint with respect to a given indefinite scalar product (i.e. pseudosymmetic matrices). The pseudosymmet…
Stable and Efficient Computation of Generalized Polar Decompositions
Peter Benner, Yuji Nakatsukasa, Carolin Penke
We present methods for computing the generalized polar decomposition of a matrix based on the dynamically weighted Halley (DWH) iteration. This method is well established for compu…
Efficient and Accurate Algorithms for Solving the Bethe-Salpeter Eigenvalue Problem for Crystalline Systems
Peter Benner, Carolin Penke
Optical properties of materials related to light absorption and scattering are explained by the excitation of electrons. The Bethe-Salpeter equation is the state-of-the-art approac…
GR decompositions and their relations to Cholesky-like factorizations
Peter Benner, Carolin Penke
For a given matrix, we are interested in computing GR decompositions , where is an isometry with respect to given scalar products. The orthogonal QR decomposition is the…
High Performance Solution of Skew-symmetric Eigenvalue Problems with Applications in Solving the Bethe-Salpeter Eigenvalue Problem
Carolin Penke, Andreas Marek, Christian Vorwerk +2
We present a high-performance solver for dense skew-symmetric matrix eigenvalue problems. Our work is motivated by applications in computational quantum physics, where one solution…