×

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


MSC:

65F15 Numerical computation of eigenvalues and eigenvectors of matrices
PDF BibTeX XML Cite
Full Text: DOI arXiv

References:

[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.