This title appears in the Scientific Report :
2020
Please use the identifier:
http://dx.doi.org/10.1137/19M1277813 in citations.
Please use the identifier: http://hdl.handle.net/2128/25754 in citations.
The LAPW Method with Eigendecomposition Based on the Hari--Zimmermann Generalized Hyperbolic SVD
The LAPW Method with Eigendecomposition Based on the Hari--Zimmermann Generalized Hyperbolic SVD
In this paper we propose an accurate, highly parallel algorithm for the generalized eigendecomposition of a matrix pair $(H, S)$, given in a factored form $(F^{\ast} J F, G^{\ast} G)$. Matrices $H$ and $S$ are generally complex and Hermitian, and $S$ is positive definite. These type of matrices emer...
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Personal Name(s): | Singer, Sanja |
---|---|
Di Napoli, Edoardo (Corresponding author) / Novaković, Vedran / Čaklović, Gayatri | |
Contributing Institute: |
Jülich Supercomputing Center; JSC |
Published in: | SIAM journal on scientific computing, 42 (2020) 5, S. C265–C293 |
Imprint: |
Philadelphia, Pa.
SIAM
2020
|
DOI: |
10.1137/19M1277813 |
Document Type: |
Journal Article |
Research Program: |
Simulation and Data Laboratory Quantum Materials (SDLQM) Doktorand ohne besondere Förderung Computational Science and Mathematical Methods |
Link: |
OpenAccess OpenAccess |
Publikationsportal JuSER |
Please use the identifier: http://hdl.handle.net/2128/25754 in citations.
In this paper we propose an accurate, highly parallel algorithm for the generalized eigendecomposition of a matrix pair $(H, S)$, given in a factored form $(F^{\ast} J F, G^{\ast} G)$. Matrices $H$ and $S$ are generally complex and Hermitian, and $S$ is positive definite. These type of matrices emerge from the representation of the Hamiltonian of a quantum mechanical system in terms of an overcomplete set of basis functions. This expansion is part of a class of models within the broad field of Density Functional Theory, which is considered the golden standard in Condensed Matter Physics. The overall algorithm consists of four phases, the second and the fourth being optional, where the two last phases are computation of the generalized hyperbolic SVD of a complex matrix pair $(F,G)$, according to a given matrix $J$ defining the hyperbolic scalar product. If $J = I$, then these two phases compute the GSVD in parallel very accurately and efficiently. |