2020/12/01 by Shengguo Li, Xinzhe Wu, Li, Shengguo +9
Chemistry · Computer Science · Mathematics · #Advanced NMR Techniques and Applications #FOS: Computer and information sciences #FOS: Mathematics #Mathematical Software (cs.MS) #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.2012.00506
openalex publication_date 2020/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, a Parallel Direct Eigensolver for Sequences of Hermitian\nEigenvalue Problems with no tridiagonalization is proposed, denoted by\n\PDESHEP, and it combines direct methods with iterative methods.\n\PDESHEP first reduces a Hermitian matrix to its banded form, then\napplies a spectrum slicing algorithm to the banded matrix, and finally computes\nthe eigenvectors of the original matrix via backtransform. Therefore, compared\nwith conventional direct eigensolvers, \PDESHEP avoids\ntridiagonalization, which consists of many memory-bounded operations. In this\nwork, the iterative method in \PDESHEP is based on the contour integral\nmethod implemented in FEAST. The combination of direct methods with iterative\nmethods for banded matrices requires some efficient data redistribution\nalgorithms both from 2D to 1D and from 1D to 2D data structures. Hence, some\ntwo-step data redistribution algorithms are proposed, which can be 10\×\nfaster than ScaLAPACK routine \PXGEMR2D. For the symmetric\nself-consistent field (SCF) eigenvalue problems, \PDESHEP can be on\naverage 1.25\× faster than the state-of-the-art direct solver in ELPA\nwhen using 4096 processes. Numerical results are obtained for dense Hermitian\nmatrices from real applications and large real sparse matrices from the\nSuiteSparse collection.\n