A robust and efficient implementation of LOBPCG. (English) Zbl 1401.65038


65F15 Numerical computation of eigenvalues and eigenvectors of matrices
Full Text: DOI arXiv


[1] H. M. Aktulga, M. Afibuzzaman, S. Williams, A. Buluç, M. Shao, C. Yang, E. G. Ng, P. Maris, and J. P. Vary, A high performance block eigensolver for nuclear configuration interaction calculations, IEEE Trans. Parallel Distrib. Syst., 28 (2017), pp. 1550–1563, .
[2] E. Anderson, Z. Bai, C. H. Bischof, L. S. Blackford, J. W. Demmel, J. J. Dongarra, J. J. Du Croz, A. Greenbaum, S. J. Hammarling, A. McKenney, and D. C. Sorensen, LAPACK Users’ Guide, 3rd ed., SIAM, Philadelphia, 1999, . · Zbl 0934.65030
[3] C. G. Baker, U. L. Hetmaniuk, R. B. Lehoucq, and H. K. Thornquist, Anasazi software for the numerical solution of large-scale eigenvalue problems, ACM Trans. Math. Software, 36 (2009), 13, . · Zbl 1364.65083
[4] G. Ballard, E. Carson, J. Demmel, M. Hoemmen, N. Knight, and O. Schwartz, Communication lower bounds and optimal algorithms for numerical linear algebra, Acta Numer., 23 (2014), pp. 1–155, . · Zbl 1396.65082
[5] J. A. Duersch, High Efficiency Spectral Analysis and BLAS-3 Randomized QRCP with Low-Rank Approximations, Ph.D. thesis, University of California, Berkeley, CA, 2015.
[6] I. S. Duff, M. A. Heroux, and R. Pozo, An overview of the sparse basic linear algebra subprograms: The new standard from the BLAS technical forum, ACM Trans. Math. Software, 28 (2002), pp. 239–267, . · Zbl 1070.65521
[7] G. H. Golub and C. F. Van Loan, Matrix Computations, 3rd ed., Johns Hopkins University Press, Baltimore, MD, 1996. · Zbl 0865.65009
[8] U. Hetmaniuk and R. Lehoucq, Basis selection in LOBPCG, J. Comput. Phys., 218 (2006), pp. 324–332, . · Zbl 1104.65031
[9] A. V. Knyazev, Toward the optimal preconditioned eigensolver: Locally optimal block preconditioned conjugate gradient method, SIAM J. Sci. Comput., 23 (2001), pp. 517–541, . · Zbl 0992.65028
[10] A. V. Knyazev, M. E. Argentati, I. Lashuk, and E. E. Ovtchinnikov, Block locally optimal preconditioned eigenvalue xolvers (BLOPEX) in hypre and PETSc, SIAM J. Sci. Comput., 29 (2007), pp. 2224–2239, . · Zbl 1149.65026
[11] L. Kronik, A. Makmal, M. L. Tiago, M. M. G. Alemany, M. Jain, X. Huang, Y. Saad, and J. R. Chelikowsky, PARSEC—the pseudopotential algorithm for real-space electronic structure calculations: recent advances and novel applications to nano-structures, Phys. Status Solidi B, 243 (2006), pp. 1063–1079, .
[12] C. L. Lawson, R. J. Hanson, D. R. Kincaid, and F. T. Krogh, Basic linear algebra subprograms for Fortran usage, ACM Trans. Math. Software, 5 (1979), pp. 308–323, . · Zbl 0412.65022
[13] R. M. Martin, Electronic Structure, Cambridge University Press, Cambridge, UK, 2004.
[14] M. Shao, H. M. Aktulga, C. Yang, E. G. Ng, P. Maris, and J. P. Vary, Accelerating nuclear configuration interaction calculations through a preconditioned block iterative eigensolver, Comput. Phys. Commun., 222 (2018), pp. 1–13, .
[15] J. M. Soler, E. Artacho, J. D. Gale, A. García, J. Junquera, P. Ordejón, and D. Sánchez-Portal, The SIESTA method for ab initio order-\(N\) materials simulation, J. Phys.: Condens. Matter, 14 (2002), 2745, .
[16] A. Stathopoulos and K. Wu, A block orthogonalization procedure with constant synchronization requirements, SIAM J. Sci. Comput., 23 (2002), pp. 2165–2182, . · Zbl 1018.65050
[17] G. W. Stewart and J.-G. Sun, Matrix Perturbation Theory, Academic Press, Boston, 1990. · Zbl 0706.65013
[18] J. H. Wilkinson, The Algebraic Eigenvalue Problem, Oxford University Press, London, 1965. · Zbl 0258.65037
[19] Y. Yamamoto, Y. Nakatsukasa, Y. Yanagisawa, and T. Fukaya, Roundoff error analysis of the CholeskyQR\(2\) algorithm, Electron. Trans. Numer. Anal., 44 (2015), pp. 306–326. · Zbl 1330.65049
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