A parallel structured banded DC algorithm for symmetric eigenvalue problems

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 struct...

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Published in:	CCF transactions on high performance computing (Online) Vol. 5; no. 2; pp. 116 - 128
Main Authors:	Li, Shengguo, Liao, Xia, Lu, Yutong, Roman, Jose E., Yue, Xiaoqiang
Format:	Journal Article
Language:	English
Published:	Singapore Springer Nature Singapore 01.06.2023 Springer Nature B.V
Subjects:	Algorithms Computer Hardware Computer Science Computer Systems Organization and Communication Networks Eigenvalues Eigenvectors Regular Paper Software Structured matrices PSMMA ScaLAPACK PBSDC 68W10 Distributed-memory parallel algorithm 65F15 Divide-and-conquer
ISSN:	2524-4922, 2524-4930
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Abstract	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.
AbstractList	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.
Author	Li, Shengguo Lu, Yutong Roman, Jose E. Yue, Xiaoqiang Liao, Xia
Author_xml	– sequence: 1 givenname: Shengguo orcidid: 0000-0001-7827-6304 surname: Li fullname: Li, Shengguo organization: College of Computer Science, National University of Defense Technology – sequence: 2 givenname: Xia surname: Liao fullname: Liao, Xia email: liaoxia@nudt.edu.cn organization: College of Computer Science, National University of Defense Technology – sequence: 3 givenname: Yutong surname: Lu fullname: Lu, Yutong organization: National Supercomputer Center in Guangzhou, and the School of Data and Computer Science, Sun Yatsen University – sequence: 4 givenname: Jose E. surname: Roman fullname: Roman, Jose E. organization: D. Sistemes Informàtics i Computació, Universitat Politècnica de València – sequence: 5 givenname: Xiaoqiang surname: Yue fullname: Yue, Xiaoqiang organization: Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education, Xiangtan University
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References	Chandrasekaran, Dewilde, Gu, Lyons, Pals (CR10) 2006; 29 Bischof, Lang, Sun (CR6) 2000; 26 Imamura, Yamada, Yoshida (CR29) 2011; 2 Zhang, Smith, Sternberg, Zapol (CR51) 2007; 33 Liao, Li, Cheng, Gu (CR36) 2016; 71 CR31 Li, Rouet, Liu, Huang, Gao, Chi (CR33) 2018; 344 Hackbusch (CR25) 1999; 62 Fox, Otto, Hey (CR17) 1987; 4 CR8 Bischof, Lang, Sun (CR5) 2000; 26 CR44 Choi, Walker, Dongarra (CR11) 1994; 6 CR43 CR42 Haidar, Ltaief, Dongarra (CR28) 2012; 34 Gu, Eisenstat (CR23) 1995; 16 Cuppen (CR12) 1981; 36 Martin (CR39) 2008 Auckenthaler, Blum, Bungartz, Huckle, Johanni, Krämer, Lang, Lederer, Willems (CR3) 2011; 37 Hackbusch, Börm (CR26) 2002; 69 Marek, Blum, Johanni, Havu, Lang, Auckenthaler, Heinecke, Bungartz, Lederer (CR38) 2014; 26 Hackbusch, Khoromskij (CR27) 2003; 70 CR19 Gu, Eisenstat (CR22) 1994; 15 Demmel (CR14) 1997 Vandebril, Van Barel, Mastronardi (CR46) 2008 CR15 Gansterer, Ward, Muller (CR20) 2002; 28 Arbenz (CR2) 1992; 18 Chandrasekaran, Dewilde, Gu, Pals, Sun, van der Veen, White (CR9) 2005; 27 Kressner, Susnjara (CR30) 2017; 38 Ambikasaran, Darve (CR1) 2013; 57 Petschow, Peise, Bientinesi (CR41) 2013; 35 Tisseur, Dongarra (CR45) 1999; 20 Davis, Hu (CR13) 2011; 38 Bunch, Nielsen, Sorensen (CR7) 1978; 31 Li, Gu, Cheng, Chi, Sun (CR32) 2014; 35 Vogel, Xia, Cauley, Balakrishnan (CR47) 2016; 38 Eidelman, Gohberg (CR16) 1999; 34 Gu, Eisenstat (CR24) 1995; 16 Wilkinson (CR48) 1965 Francis (CR18) 1962; 4 CR21 Xia, Chandrasekaran, Gu, Li (CR50) 2009; 31 Liao, Xiao, Yang, Lu (CR34) 2014; 8 Liao, Pang, Wang, Lu, Xie, Xia, Dong, Suo (CR35) 2015; 30 Liao, Li, Lu, Roman (CR37) 2021; 32 Parlett (CR40) 1998 Willems, Lang (CR49) 2013; 35 Bai, Ward (CR4) 2007; 33 S Chandrasekaran (117_CR9) 2005; 27 117_CR44 117_CR43 117_CR42 X Liao (117_CR36) 2016; 71 T Auckenthaler (117_CR3) 2011; 37 A Haidar (117_CR28) 2012; 34 F Tisseur (117_CR45) 1999; 20 S Ambikasaran (117_CR1) 2013; 57 J Xia (117_CR50) 2009; 31 M Gu (117_CR23) 1995; 16 PR Willems (117_CR49) 2013; 35 T Imamura (117_CR29) 2011; 2 CH Bischof (117_CR5) 2000; 26 RM Martin (117_CR39) 2008 117_CR19 M Gu (117_CR22) 1994; 15 W Hackbusch (117_CR26) 2002; 69 YH Bai (117_CR4) 2007; 33 117_CR15 T Davis (117_CR13) 2011; 38 M Petschow (117_CR41) 2013; 35 D Kressner (117_CR30) 2017; 38 JG Francis (117_CR18) 1962; 4 WN Gansterer (117_CR20) 2002; 28 CH Bischof (117_CR6) 2000; 26 X Liao (117_CR34) 2014; 8 J Demmel (117_CR14) 1997 LGW Hackbusch (117_CR27) 2003; 70 117_CR21 W Hackbusch (117_CR25) 1999; 62 JJM Cuppen (117_CR12) 1981; 36 J Choi (117_CR11) 1994; 6 Y Eidelman (117_CR16) 1999; 34 JR Bunch (117_CR7) 1978; 31 X Liao (117_CR35) 2015; 30 S Li (117_CR33) 2018; 344 BN Parlett (117_CR40) 1998 117_CR8 R Vandebril (117_CR46) 2008 A Marek (117_CR38) 2014; 26 117_CR31 J Wilkinson (117_CR48) 1965 S Chandrasekaran (117_CR10) 2006; 29 H Zhang (117_CR51) 2007; 33 J Vogel (117_CR47) 2016; 38 X Liao (117_CR37) 2021; 32 P Arbenz (117_CR2) 1992; 18 S Li (117_CR32) 2014; 35 GC Fox (117_CR17) 1987; 4 M Gu (117_CR24) 1995; 16
References_xml	– volume: 2 start-page: 643 year: 2011 end-page: 650 ident: CR29 article-title: Development of a high-performance eigensolver on a peta-scale next-generation supercomputer system publication-title: Prog. Nucl. Sci. Technol. doi: 10.15669/pnst.2.643 – volume: 35 start-page: A740 issue: 2 year: 2013 end-page: A766 ident: CR49 article-title: A framework for the algorithm: theory and implementation publication-title: SIAM J. Sci. Comput. doi: 10.1137/110834020 – volume: 69 start-page: 1 year: 2002 end-page: 35 ident: CR26 article-title: Data-sparse approximation by adaptive -matrices publication-title: Computing doi: 10.1007/s00607-002-1450-4 – volume: 57 start-page: 477 issue: 3 year: 2013 end-page: 501 ident: CR1 article-title: An fast direct solver for partial hierarchically semi-separable matrices publication-title: J. Sci. Comput. doi: 10.1007/s10915-013-9714-z – ident: CR8 – volume: 4 start-page: 17 issue: 1 year: 1987 end-page: 31 ident: CR17 article-title: Matrix algorithms on a hypercube I: matrix multiplication publication-title: Parallel Comput. doi: 10.1016/0167-8191(87)90060-3 – ident: CR42 – volume: 28 start-page: 45 issue: 1 year: 2002 end-page: 58 ident: CR20 article-title: An extension of the divide-and-conquer method for a class of symmetric block-tridiagonal eigenproblems publication-title: ACM Trans. Math. Softw. doi: 10.1145/513001.513004 – volume: 8 start-page: 345 issue: 3 year: 2014 end-page: 356 ident: CR34 article-title: Milkyway-2 supercomputer: system and application publication-title: Front. Comput. Sci. doi: 10.1007/s11704-014-3501-3 – ident: CR21 – volume: 32 start-page: 367 issue: 2 year: 2021 end-page: 378 ident: CR37 article-title: A parallel structured divide-and-conquer algorithm for symmetric tridiagonal eigenvalue problems publication-title: IEEE Trans. Parallel Distrib. Syst. doi: 10.1109/TPDS.2020.3019471 – volume: 27 start-page: 341 year: 2005 end-page: 364 ident: CR9 article-title: Some fast algorithms for sequentially semiseparable representation publication-title: SIAM J. Matrix Anal. Appl. doi: 10.1137/S0895479802405884 – ident: CR19 – volume: 33 start-page: 1 issue: 4 year: 2007 end-page: 23 ident: CR4 article-title: A parallel symmetric block-tridiagonal divide-and-conquer algorithm publication-title: ACM Trans. Math. Softw. doi: 10.1145/1268776.1268780 – volume: 35 start-page: 1038 issue: 3 year: 2014 end-page: 1057 ident: CR32 article-title: An accelerated divide-and-conquer algorithm for the bidiagonal SVD problem publication-title: SIAM J. Matrix Anal. Appl. doi: 10.1137/130945995 – ident: CR15 – volume: 62 start-page: 89 year: 1999 end-page: 108 ident: CR25 article-title: A sparse matrix arithmetic based on -matrices. Part I: introduction to -matrices publication-title: Computing doi: 10.1007/s006070050015 – volume: 71 start-page: 1933 year: 2016 end-page: 1943 ident: CR36 article-title: An improved divide-and-conquer algorithm for the banded matrices with narrow bandwidths publication-title: Comput. Math. Appl. doi: 10.1016/j.camwa.2016.03.008 – volume: 15 start-page: 1266 year: 1994 end-page: 1276 ident: CR22 article-title: A stable and efficient algorithm for the rank-one modification of the symmetric eigenproblem publication-title: SIAM J. Matrix Anal. Appl. doi: 10.1137/S089547989223924X – volume: 70 start-page: 121 year: 2003 end-page: 165 ident: CR27 article-title: Solution of large scale algebraic matrix Riccati equations by use of hierarchical matrices publication-title: Computing doi: 10.1007/s00607-002-1470-0 – year: 2008 ident: CR39 publication-title: Electronic Structure: Basic Theory and Practical Methods – year: 2008 ident: CR46 publication-title: Matrix Computations and Semiseparable Matrices, Volume I: linear systems doi: 10.1353/book.3417 – volume: 26 start-page: 581 issue: 4 year: 2000 end-page: 601 ident: CR5 article-title: A framework for symmetric band reduction publication-title: ACM Trans. Math. Softw. doi: 10.1145/365723.365735 – volume: 6 start-page: 543 issue: 7 year: 1994 end-page: 570 ident: CR11 article-title: Pumma: Parallel universal matrix multiplication algorithms on distributed memory concurrent computers publication-title: Concurr. Comput. Pract. Exper. doi: 10.1002/cpe.4330060702 – volume: 34 start-page: 293 year: 1999 end-page: 324 ident: CR16 article-title: On a new class of structured matrices publication-title: Integr. Eqn. Oper. Theory doi: 10.1007/BF01300581 – ident: CR43 – volume: 35 start-page: C1 year: 2013 end-page: C22 ident: CR41 article-title: High-performance solvers for dense Hermitian eigenproblems publication-title: SIAM J. Numer. Anal. – volume: 38 start-page: 1:1 issue: 1 year: 2011 end-page: 1:25 ident: CR13 article-title: The University of Florida sparse matrix collection publication-title: ACM Trans. Math. Softw. doi: 10.1145/2049662.2049663 – year: 1998 ident: CR40 publication-title: The Symmetric Eigenvalue Problem doi: 10.1137/1.9781611971163 – volume: 26 start-page: 1 year: 2014 end-page: 15 ident: CR38 article-title: The ELPA library: scalable parallel eigenvalue solutions for electronic structure theory and computational science publication-title: J. Phys. Condens. Matter doi: 10.1088/0953-8984/26/21/213201 – volume: 38 start-page: 984 issue: 3 year: 2017 end-page: 1009 ident: CR30 article-title: Fast computation of spectral projectors of banded matrices publication-title: SIAM J. Matrix Anal. Appl. doi: 10.1137/16M1087278 – volume: 344 start-page: 512 year: 2018 end-page: 520 ident: CR33 article-title: An efficient hybrid tridiagonal divide-and-conquer algorithm on distributed memory architectures publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2018.05.051 – volume: 37 start-page: 783 issue: 12 year: 2011 end-page: 794 ident: CR3 article-title: Parallel solution of partial symmetric eigenvalue problems from electronic structure calculations publication-title: Parallel Comput. doi: 10.1016/j.parco.2011.05.002 – year: 1997 ident: CR14 publication-title: Applied Numerical Linear Algebra doi: 10.1137/1.9781611971446 – volume: 33 start-page: 1 issue: 2 year: 2007 end-page: 19 ident: CR51 article-title: SIPs: shift-and-invert parallel spectral transformations publication-title: ACM Trans. Math. Softw. (TOMS) doi: 10.1145/1236463.1236464 – volume: 18 start-page: 1105 year: 1992 end-page: 1128 ident: CR2 article-title: Divide-and-conquer algorithms for the bandsymmetric eigenvalue problem publication-title: Parallel Comput. doi: 10.1016/0167-8191(92)90059-G – volume: 16 start-page: 172 year: 1995 end-page: 191 ident: CR24 article-title: A divide-and-conquer algorithm for the symmetric tridiagonal eigenproblem publication-title: SIAM J. Matrix Anal. Appl. doi: 10.1137/S0895479892241287 – ident: CR44 – volume: 31 start-page: 1382 year: 2009 end-page: 1411 ident: CR50 article-title: Superfast multifrontal method for large structured linear systems of equation publication-title: SIAM J. Matrix Anal. Appl. doi: 10.1137/09074543X – volume: 26 start-page: 602 issue: 4 year: 2000 end-page: 616 ident: CR6 article-title: Algorithm 807: the SBR toolbox-software for successive band reduction publication-title: ACM Trans. Math. Softw. doi: 10.1145/365723.365736 – volume: 30 start-page: 259 issue: 2 year: 2015 end-page: 272 ident: CR35 article-title: High performance interconnect network for Tianhe system publication-title: J. Comput. Sci. Tech. doi: 10.1007/s11390-015-1520-7 – volume: 29 start-page: 67 year: 2006 end-page: 81 ident: CR10 article-title: A fast solver for HSS representations via sparse matrices publication-title: SIAM J. Matrix Anal. Appl. doi: 10.1137/050639028 – volume: 38 start-page: A1358 issue: 3 year: 2016 end-page: A1382 ident: CR47 article-title: Superfast divide-and-conquer method and perturbation analysis for structured eigenvalue solutions publication-title: SIAM J. Sci. Comput. doi: 10.1137/15M1018812 – volume: 31 start-page: 31 year: 1978 end-page: 48 ident: CR7 article-title: Rank one modification of the symmetric eigenproblem publication-title: Numer. Math. doi: 10.1007/BF01396012 – ident: CR31 – volume: 20 start-page: 2223 issue: 6 year: 1999 end-page: 2236 ident: CR45 article-title: A parallel divide and conquer algorithm for the symmetric eigenvalue problem on distributed memory architectures publication-title: SIAM J. Sci. Comput. doi: 10.1137/S1064827598336951 – volume: 4 start-page: 332 issue: 4 year: 1962 end-page: 345 ident: CR18 article-title: The QR transformation-part 2 publication-title: Comput. J. doi: 10.1093/comjnl/4.4.332 – volume: 16 start-page: 79 issue: 1 year: 1995 end-page: 92 ident: CR23 article-title: A divide-and-conquer algorithm for the bidiagonal SVD publication-title: SIAM J. Matrix Anal. Appl. doi: 10.1137/S0895479892242232 – year: 1965 ident: CR48 publication-title: The Algebraic Eigenvalue Problem – volume: 36 start-page: 177 year: 1981 end-page: 195 ident: CR12 article-title: A divide and conquer method for the symmetric tridiagonal eigenproblem publication-title: Numer. Math. doi: 10.1007/BF01396757 – volume: 34 start-page: C249 issue: 6 year: 2012 end-page: C274 ident: CR28 article-title: Toward a high performance tile divide and conquer algorithm for the dense symmetric eigenvalue problem publication-title: SIAM J. Sci. Comput. doi: 10.1137/110823699 – volume: 36 start-page: 177 year: 1981 ident: 117_CR12 publication-title: Numer. Math. doi: 10.1007/BF01396757 – ident: 117_CR8 – volume: 4 start-page: 332 issue: 4 year: 1962 ident: 117_CR18 publication-title: Comput. J. doi: 10.1093/comjnl/4.4.332 – volume: 34 start-page: 293 year: 1999 ident: 117_CR16 publication-title: Integr. Eqn. Oper. Theory doi: 10.1007/BF01300581 – volume: 70 start-page: 121 year: 2003 ident: 117_CR27 publication-title: Computing doi: 10.1007/s00607-002-1470-0 – ident: 117_CR15 – volume: 26 start-page: 581 issue: 4 year: 2000 ident: 117_CR5 publication-title: ACM Trans. Math. Softw. doi: 10.1145/365723.365735 – ident: 117_CR42 doi: 10.1109/IPDPS.2015.51 – volume: 32 start-page: 367 issue: 2 year: 2021 ident: 117_CR37 publication-title: IEEE Trans. Parallel Distrib. Syst. doi: 10.1109/TPDS.2020.3019471 – volume: 31 start-page: 1382 year: 2009 ident: 117_CR50 publication-title: SIAM J. Matrix Anal. Appl. doi: 10.1137/09074543X – volume: 16 start-page: 172 year: 1995 ident: 117_CR24 publication-title: SIAM J. Matrix Anal. Appl. doi: 10.1137/S0895479892241287 – volume: 31 start-page: 31 year: 1978 ident: 117_CR7 publication-title: Numer. Math. doi: 10.1007/BF01396012 – volume: 38 start-page: 1:1 issue: 1 year: 2011 ident: 117_CR13 publication-title: ACM Trans. Math. Softw. doi: 10.1145/2049662.2049663 – volume: 35 start-page: C1 year: 2013 ident: 117_CR41 publication-title: SIAM J. Numer. Anal. – ident: 117_CR31 – volume: 71 start-page: 1933 year: 2016 ident: 117_CR36 publication-title: Comput. Math. Appl. doi: 10.1016/j.camwa.2016.03.008 – volume: 38 start-page: A1358 issue: 3 year: 2016 ident: 117_CR47 publication-title: SIAM J. Sci. Comput. doi: 10.1137/15M1018812 – volume: 28 start-page: 45 issue: 1 year: 2002 ident: 117_CR20 publication-title: ACM Trans. Math. Softw. doi: 10.1145/513001.513004 – volume: 38 start-page: 984 issue: 3 year: 2017 ident: 117_CR30 publication-title: SIAM J. Matrix Anal. Appl. doi: 10.1137/16M1087278 – volume: 33 start-page: 1 issue: 2 year: 2007 ident: 117_CR51 publication-title: ACM Trans. Math. Softw. (TOMS) doi: 10.1145/1236463.1236464 – volume: 2 start-page: 643 year: 2011 ident: 117_CR29 publication-title: Prog. Nucl. Sci. Technol. doi: 10.15669/pnst.2.643 – volume: 344 start-page: 512 year: 2018 ident: 117_CR33 publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2018.05.051 – ident: 117_CR21 – volume: 16 start-page: 79 issue: 1 year: 1995 ident: 117_CR23 publication-title: SIAM J. Matrix Anal. Appl. doi: 10.1137/S0895479892242232 – volume: 29 start-page: 67 year: 2006 ident: 117_CR10 publication-title: SIAM J. Matrix Anal. Appl. doi: 10.1137/050639028 – volume: 20 start-page: 2223 issue: 6 year: 1999 ident: 117_CR45 publication-title: SIAM J. Sci. Comput. doi: 10.1137/S1064827598336951 – volume: 37 start-page: 783 issue: 12 year: 2011 ident: 117_CR3 publication-title: Parallel Comput. doi: 10.1016/j.parco.2011.05.002 – volume-title: The Algebraic Eigenvalue Problem year: 1965 ident: 117_CR48 – volume: 4 start-page: 17 issue: 1 year: 1987 ident: 117_CR17 publication-title: Parallel Comput. doi: 10.1016/0167-8191(87)90060-3 – volume: 27 start-page: 341 year: 2005 ident: 117_CR9 publication-title: SIAM J. Matrix Anal. Appl. doi: 10.1137/S0895479802405884 – volume: 34 start-page: C249 issue: 6 year: 2012 ident: 117_CR28 publication-title: SIAM J. Sci. Comput. doi: 10.1137/110823699 – volume: 69 start-page: 1 year: 2002 ident: 117_CR26 publication-title: Computing doi: 10.1007/s00607-002-1450-4 – volume: 35 start-page: 1038 issue: 3 year: 2014 ident: 117_CR32 publication-title: SIAM J. Matrix Anal. Appl. doi: 10.1137/130945995 – volume: 35 start-page: A740 issue: 2 year: 2013 ident: 117_CR49 publication-title: SIAM J. Sci. Comput. doi: 10.1137/110834020 – volume: 8 start-page: 345 issue: 3 year: 2014 ident: 117_CR34 publication-title: Front. Comput. Sci. doi: 10.1007/s11704-014-3501-3 – volume-title: Electronic Structure: Basic Theory and Practical Methods year: 2008 ident: 117_CR39 – volume: 15 start-page: 1266 year: 1994 ident: 117_CR22 publication-title: SIAM J. Matrix Anal. Appl. doi: 10.1137/S089547989223924X – volume-title: Applied Numerical Linear Algebra year: 1997 ident: 117_CR14 doi: 10.1137/1.9781611971446 – volume: 6 start-page: 543 issue: 7 year: 1994 ident: 117_CR11 publication-title: Concurr. Comput. Pract. Exper. doi: 10.1002/cpe.4330060702 – volume: 26 start-page: 602 issue: 4 year: 2000 ident: 117_CR6 publication-title: ACM Trans. Math. Softw. doi: 10.1145/365723.365736 – volume: 30 start-page: 259 issue: 2 year: 2015 ident: 117_CR35 publication-title: J. Comput. Sci. Tech. doi: 10.1007/s11390-015-1520-7 – ident: 117_CR43 doi: 10.1145/2930660 – volume: 33 start-page: 1 issue: 4 year: 2007 ident: 117_CR4 publication-title: ACM Trans. Math. Softw. doi: 10.1145/1268776.1268780 – ident: 117_CR44 – volume-title: The Symmetric Eigenvalue Problem year: 1998 ident: 117_CR40 doi: 10.1137/1.9781611971163 – ident: 117_CR19 doi: 10.1137/S1064827501399432 – volume: 26 start-page: 1 year: 2014 ident: 117_CR38 publication-title: J. Phys. Condens. Matter doi: 10.1088/0953-8984/26/21/213201 – volume: 62 start-page: 89 year: 1999 ident: 117_CR25 publication-title: Computing doi: 10.1007/s006070050015 – volume-title: Matrix Computations and Semiseparable Matrices, Volume I: linear systems year: 2008 ident: 117_CR46 doi: 10.1353/book.3417 – volume: 57 start-page: 477 issue: 3 year: 2013 ident: 117_CR1 publication-title: J. Sci. Comput. doi: 10.1007/s10915-013-9714-z – volume: 18 start-page: 1105 year: 1992 ident: 117_CR2 publication-title: Parallel Comput. doi: 10.1016/0167-8191(92)90059-G
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Snippet	In this paper, a novel parallel structured divide-and-conquer (DC) algorithm is proposed for symmetric banded eigenvalue problems, denoted by PBSDC, which...
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SubjectTerms	Algorithms Computer Hardware Computer Science Computer Systems Organization and Communication Networks Eigenvalues Eigenvectors Regular Paper Software Structured matrices
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Title	A parallel structured banded DC algorithm for symmetric eigenvalue problems
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