A parallel structured banded DC algorithm for symmetric eigenvalue problems

被引：2
作者：
Li, Shengguo [1 ]
Liao, Xia [1 ]
Lu, Yutong [2 ,3 ]
Roman, Jose E. [4 ]
Yue, Xiaoqiang [5 ]
机构：
[1] Natl Univ Def Technol, Coll Comp Sci, Changsha 410073, Peoples R China
[2] Sun Yatsen Univ, Natl Supercomp Ctr Guangzhou, Guangzhou 510006, Peoples R China
[3] Sun Yatsen Univ, Sch Data & Comp Sci, Guangzhou 510006, Peoples R China
[4] Univ Politecn Valencia, D Sistemes Informat & Comp, Cami Vera S-N, Valencia 46022, Spain
[5] Xiangtan Univ, Hunan Key Lab Computat & Simulat Sci & Engn, Key Lab Intelligent Comp & Informat Proc, Minist Educ, Xiangtan 411105, Peoples R China
来源：
CCF TRANSACTIONS ON HIGH PERFORMANCE COMPUTING | 2023年 / 5卷 / 02期
关键词：
ScaLAPACK; Divide-and-conquer; PSMMA; PBSDC; Distributed-memory parallel algorithm; RANK-ONE MODIFICATION; CONQUER ALGORITHM; DIVIDE; FRAMEWORK;
D O I：
10.1007/s42514-022-00117-9
中图分类号：
TP3 [计算技术、计算机技术];
学科分类号：
0812 ;
摘要：
In this paper, a novel parallel structured divide-and-conquer (DC) algorithm is proposed for symmetric banded eigenvalue problems, denoted by PBSDC, which modifies the classical parallel banded DC (PBDC) algorithm by reducing its computational cost. The main tool that PBSDC uses is a parallel structured matrix multiplication algorithm (PSMMA), which can be much faster than the general dense matrix multiplication ScaLAPACK routine PDGEMM. Numerous experiments have been performed on Tianhe-2 supercomputer to compare PBSDC with PBDC and ELPA. For matrices with few deflations, PBSDC can be much faster than PBDC since computations are saved. For matrices with many deflations and/or small bandwidths, PBSDC can be faster than the tridiagonalization-based DC implemented in LAPACK and ELPA. However, PBSDC would become slower than ELPA for matrices with relatively large bandwidths.
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页码：116 / 128
页数：13
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