Journal Article

FZJ-2019-04005

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png The LAPW Method with Eigendecomposition Based on the Hari--Zimmermann Generalized Hyperbolic SVD

Singer, S. ; Di Napoli, E. (Corresponding author)FZJ* ; Novaković, V. ; Čaklović, G.FZJ*

2020
SIAM Philadelphia, Pa.

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Please use a persistent id in citations: http://hdl.handle.net/2128/25754  doi:10.1137/19M1277813

Abstract: 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.

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Contributing Institute(s):

1. Jülich Supercomputing Center (JSC)

Research Program(s):

1. 511 - Computational Science and Mathematical Methods (POF3-511) (POF3-511)
2. PhD no Grant - Doktorand ohne besondere Förderung (PHD-NO-GRANT-20170405) (PHD-NO-GRANT-20170405)
3. Simulation and Data Laboratory Quantum Materials (SDLQM) (SDLQM) (SDLQM)

Appears in the scientific report 2020

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Database coverage:
; ; Clarivate Analytics Master Journal List ; Current Contents - Physical, Chemical and Earth Sciences ; Ebsco Academic Search ; IF < 5 ; JCR ; SCOPUS ; Science Citation Index ; Science Citation Index Expanded ; Web of Science Core Collection

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