swMATH ID: 24008
Software Authors: Knyazev, Andrew V.
Description: lobpcg.m, MATLAB implementation of the locally optimal block preconditioned conjugate gradient method: Toward the optimal preconditioned eigensolver: Locally optimal block preconditioned conjugate gradient method. We describe new algorithms of the locally optimal block preconditioned conjugate gradient (LOBPCG) method for symmetric eigenvalue problems, based on a local optimization of a three-term recurrence, and suggest several other new methods. To be able to compare numerically different methods in the class, with different preconditioners, we propose a common system of model tests, using random preconditioners and initial guesses. As the “ideal” control algorithm, we advocate the standard preconditioned conjugate gradient method for finding an eigenvector as an element of the null-space of the corresponding homogeneous system of linear equations under the assumption that the eigenvalue is known. We recommend that every new preconditioned eigensolver be compared with this “ideal” algorithm on our model test problems in terms of the speed of convergence, costs of every iteration, and memory requirements. We provide such comparison for our LOBPCG method. Numerical results establish that our algorithm is practically as efficient as the “ideal” algorithm when the same preconditioner is used in both methods. We also show numerically that the LOBPCG method provides approximations to first eigenpairs of about the same quality as those by the much more expensive global optimization method on the same generalized block Krylov subspace. We propose a new version of block Davidson’s method as a generalization of the LOBPCG method. Finally, direct numerical comparisons with the Jacobi-Davidson method show that our method is more robust and converges almost two times faster.
Homepage: https://www.mathworks.com/matlabcentral/fileexchange/48-lobpcg-m
Related Software: JDQZ; JDQR; ARPACK; BLOPEX; EIGIFP; PRIMME; FEAST; IRAM; LAPACK; eigs; Matlab; KSSOLV; SparseMatrix; SLEPc; JDCG; Quantum Espresso; PETSc; TRLan; ABINIT; PARSEC
Cited in: 167 Documents
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Cited by 297 Authors

12 Lin, Lin
8 Yang, Chao
6 Li, Rencang
6 Miao, Cun-Qiang
6 Wen, Zaiwen
5 Knyazev, Andrew V.
5 Nakatsukasa, Yuji
5 Sousedík, Bedřich
5 Zhang, Lei-Hong
5 Zhang, Lei
4 Hu, Guanghui
4 Li, Yingzhou
4 Liu, Xin
4 Lu, Jianfeng
4 Neymeyr, Klaus
4 Shao, Meiyue
4 Vecharynski, Eugene
4 Zhang, Yin
4 Zhou, Yunkai
3 Bergamaschi, Luca
3 Huang, Tsungming
3 Klawonn, Axel
3 Kressner, Daniel
3 Kuang, Yang
3 Levitt, Antoine
3 Mandel, Jan
3 Ovtchinnikov, Evgueni Eduardovich
3 Pini, Giorgio
3 Rheinbach, Oliver
3 Saad, Yousef
3 Stathopoulos, Andreas
3 Wang, Li
3 Xie, Hehu
3 Yin, Jianyuan
3 Ying, Lexing
3 Zhang, Pingwen
2 Aishima, Kensuke
2 Cancès, Eric
2 Chen, Wenbin
2 Dolgov, Sergey V.
2 E, Weinan
2 Gao, Weiguo
2 Hwang, Fengnan
2 Imakura, Akira
2 Kemlin, Gaspard
2 Khoromskiĭ, Boris Nikolaevich
2 Kühn, Martin Joachim
2 Lehoucq, Richard B.
2 Lu, Zhongjie
2 Martínez, Ángeles
2 Oseledets, Ivan Valer’evich
2 Pavarino, Luca Franco
2 Pollock, Sara
2 Román, Jose E.
2 Romero, Eloy
2 Shao, Nian
2 Shen, Chungen
2 Šístek, Jakub
2 Spence, Alastair
2 Wang, Lin-Wang
2 Wang, Weichung
2 Wei, Zih-Hao
2 Xu, Ze
2 Xue, Fei
2 Ye, Qiang
2 Zhang, Shao-Liang
2 Zhou, Ming
1 Abdel-Rehim, Abdou M.
1 Abdelmoula, Radhi
1 Ainsworth, Mark
1 Altmann, Robert
1 An, Dong
1 Antoine, Xavier
1 Arbenz, Peter
1 Argentati, Merico E.
1 Bai, Zhaojun
1 Baker, C. G.
1 Banerjee, Amartya S.
1 Bao, Gang
1 Beams, Natalie N.
1 Beecroft, Damien
1 Benner, Peter
1 Bernholc, J.
1 Berns-Müller, Jörg
1 Binante, Vincenzo
1 Boffi, Daniele
1 Bollhöfer, Matthias
1 Bozzo, Enrico
1 Bramble, James H.
1 Briggs, E. L.
1 Cai, Jian-Feng
1 Canning, Andrew
1 Carson, Erin Claire
1 Chelikowsky, James R.
1 Cheng, Lan
1 Cheng, Xiangle
1 Cho, Heyrim
1 Chung, Tsz Shun Eric
1 Cichocki, Andrzej
1 Cucuringu, Mihai
...and 197 more Authors
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Cited in 56 Serials

27 SIAM Journal on Scientific Computing
21 Journal of Computational Physics
12 Linear Algebra and its Applications
9 Journal of Scientific Computing
7 SIAM Journal on Matrix Analysis and Applications
6 Mathematics of Computation
6 Journal of Computational and Applied Mathematics
5 Numerische Mathematik
5 Numerical Algorithms
4 Computer Methods in Applied Mechanics and Engineering
4 Multiscale Modeling & Simulation
4 Science China. Mathematics
3 SIAM Journal on Numerical Analysis
3 Japan Journal of Industrial and Applied Mathematics
3 Communications in Computational Physics
2 Computers & Mathematics with Applications
2 Computer Physics Communications
2 Applied Mathematics and Computation
2 Numerical Linear Algebra with Applications
2 Advances in Computational Mathematics
2 Acta Numerica
1 Computers and Fluids
1 Letters in Mathematical Physics
1 Nonlinearity
1 Wave Motion
1 ACM Transactions on Mathematical Software
1 Calcolo
1 Computing
1 International Journal for Numerical Methods in Engineering
1 Journal of Optimization Theory and Applications
1 Mathematics and Computers in Simulation
1 Journal of Computational Mathematics
1 Physica D
1 Applied Numerical Mathematics
1 Applications of Mathematics
1 Journal of Elasticity
1 Pattern Recognition
1 SIAM Journal on Optimization
1 Communications in Numerical Methods in Engineering
1 Computational and Applied Mathematics
1 ETNA. Electronic Transactions on Numerical Analysis
1 Mathematical Problems in Engineering
1 Mathematical & Computational Applications
1 Computational Geosciences
1 Computational Methods in Applied Mathematics
1 Journal of Applied Mathematics
1 Journal of Machine Learning Research (JMLR)
1 International Journal of Numerical Analysis and Modeling
1 Mathematical Programming Computation
1 Numerical Algebra, Control and Optimization
1 S\(\vec{\text{e}}\)MA Journal
1 East Asian Journal on Applied Mathematics
1 Nanoscale Systems: Mathematical Modeling, Theory and Applications
1 Research in the Mathematical Sciences
1 Results in Applied Mathematics

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