Journal Article

FZJ-2026-01049

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png PHIDE: A Parallel Hybrid Direct–Iterative Eigensolver for Hermitian Eigenvalue Problems

Li, S. ; Wu, X.FZJ* ; Roman, J. E. ; Yuan, Z. ; Wang, R. ; Li, T. ; Xie, Y. ; Yang, B. ; Chen, X. (Corresponding author)

2026
IEEE New York, NY

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Please use a persistent id in citations: doi:10.1109/TPDS.2025.3623188

Abstract: In this paper, we propose a Parallel Hybrid Direct–Iterative Eigensolver for Hermitian Eigenvalue Problems with-out tridiagonalization, denoted by PHIDE, which combines directand iterative methods. PHIDE first reduces a Hermitian matrixto banded form, then applies a spectrum slicing algorithm tothe banded matrix, and finally computes the eigenvectors of theoriginal matrix via backtransformation. Compared with conven-tional direct eigensolvers, PHIDE avoids tridiagonalization, whichinvolves many memory-bound operations. In PHIDE, the bandedeigenvalue problem is solved using the contour integral methodimplemented in FEAST, which may yield slightly lower accuracythan tridiagonalization-based approaches. For sequences of corre-lated Hermitian eigenvalue problems arising in density functionaltheory (DFT), PHIDE achieves an average speedup of $1.22×$ overthe state-of-the-art direct solver in ELPA when using 1024 pro-cesses. Numerical experiments are conducted on dense Hermitianmatrices from real applications as well as large sparse matricesfrom the SuiteSparse and ELSES collections.

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Contributing Institute(s):

1. Jülich Supercomputing Center (JSC)

Research Program(s):

1. 5111 - Domain-Specific Simulation & Data Life Cycle Labs (SDLs) and Research Groups (POF4-511) (POF4-511)

Appears in the scientific report 2026

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Database coverage:
; Clarivate Analytics Master Journal List ; Current Contents - Engineering, Computing and Technology ; Ebsco Academic Search ; Essential Science Indicators ; IF >= 5 ; JCR ; SCOPUS ; Science Citation Index Expanded ; Web of Science Core Collection

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