[EN] In this paper, a novel parallel structured divide-and-conquer (DC) algorithm is proposed for symmetric banded eigenvalue problems, denoted by PBSDC, which modifes 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 defations, PBSDC can be much faster than PBDC since computations are saved. For matrices with many defations 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.

The authors would like to thank the referees for their valuable comments. This work is supported in part by NSFC (No. 2021YFB0300101, 62073333, 61902411, 62032023, 12002382, 11275269, 42104078), 173 Program of China (2020-JCJQ-ZD-029), Open Research Fund from State Key Laboratory of High Performance Computing of China (HPCL) (No. 202101-01), Guangdong Natural Science Foundation (2018B030312002), and the Program for Guangdong Introducing Innovative and Entrepreneurial Teams under Grant (No. 2016ZT06D211). Jose E. Roman is supported by the Spanish Agencia Estatal de Investigacion (AEI) under project SLEPc-DA (PID2019-107379RB-I00). On behalf of all authors, the corresponding author states that there is no conflict of interest.