Carolin Penke

Carolin Penke
Helmholtz-Zentrum Berlin | HZB · Information Technology - Experiment Control and Data Acquisition

Master of Science

About

11
Publications
676
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13
Citations

Publications

Publications (11)
Preprint
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 pseudosymmetric structure of the matrix is preserved in the spectral division, such that the method can be applied recursively to achieve full diagonalization. The method is well-sui...
Article
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 approach to describe these processes from first principles (ab initio), i.e. without the need for empirical data in the model. To harness the predictive power of the equation, i...
Preprint
Full-text available
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 computing the standard polar decomposition. A stable implementation is available, where matrix inversion is avoided and QR decompositions are used instead. We establish a natu...
Article
Full-text available
For a given matrix, we are interested in computing GR decompositions A = GR, where G is an isometry with respect to given scalar products. The orthogonal QR decomposition is the representative for the Euclidian scalar product. For a signature matrix, a respective factorization is given as the hyperbolic QR decomposition. Considering a skew‐symmetri...
Preprint
Full-text available
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 approach to describe these processes from first principles (ab initio), i.e. without the need for empirical data in the model. To harness the predictive power of the equation, i...
Preprint
Full-text available
For a given matrix, we are interested in computing GR decompositions $A=GR$, where $G$ is an isometry with respect to given scalar products. The orthogonal QR decomposition is the representative for the Euclidian scalar product. For a signature matrix, a respective factorization is given as the hyperbolic QR decomposition. Considering a skew-symmet...
Article
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 approach to solve the Bethe-Salpeter equation involves the solution of a large, dense, skew-symmetric eigenvalue problem. The computed eigenpairs can be used to compute...
Preprint
Full-text available
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 approach to solve the so-called Bethe-Salpeter equation involves the solution of a large, dense, skew-symmetric eigenvalue problem. The computed eigenpairs can be used t...
Article
The Bethe‐Salpeter eigenvalue problem arises in the computation of the electronic structure of many‐body physical systems. The resulting matrix is complex, admits a certain block structure and can become extremely large. This raises the need for structure‐preserving algorithms running in parallel on high performance compute clusters. In this paper...
Conference Paper
The LAPACK routines GEQRT2 and GEQRT3 can be used to compute the QR decomposition of a matrix of size m×n as well as the storage-efficient representation of the orthogonal factor . A GPU-accelerated algorithm is presented that expands a blocked CPU-GPU hybrid QR decomposition to compute the triangular matrix T. The storage-efficient representation...
Article
Full-text available
The solution of linear systems of equations with many right hand sides is mostly seen as a trivial extension of solving a linear system and the algorithmic developments mostly focus on the efficient computation of the LU decomposition. This is, however, not regarding the case where many right hand sides increase the runtime influence of the forward...

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