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Performance evaluation of the Sakurai-Sugiura method with a block Krylov subspace linear solver for large dense Hermitian-definite generalized eigenvalue problems. (English) Zbl 07037372
Summary: Contour-integral based eigensolvers have been proposed for efficiently exploiting the performance of massively parallel computational environments. In the algorithms of these methods, inner linear systems need to be solved and its calculation time becomes the most time-consuming part for large-scale problems. In this paper, we consider applying a contour-integral based method to a large dense problem in conjunction with a block Krylov subspace method as an inner linear solver. Comparison of parallel performance with the contour-integral based method with a direct linear solver and a ScaLAPACK’s eigensolver is shown using matrices from a practical application.
MSC:
65 Numerical analysis
68 Computer science
Software:
ELPA
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[1] T. Sakurai; H. Sugiura, A projection method for generalized eigenvalue problems using numerical integration, J. Comput. Appl. Math., 159, 119-128, (2003) · Zbl 1037.65040
[2] T. Ikegami; T. Sakurai, Contour integral eigensolver for non-Hermitian systems: a Rayleigh-Ritz-type approach, Taiwanese J. Math., 14, 825-837, (2010) · Zbl 1198.65071
[3] A. Marek; V. Blum; R. Johanni; V. Havu; B. Lang; T. Auckenthaler; A. Heinecke; H.-J. Bungartz; H. Lederer, The ELPA library - scalable parallel eigenvalue solutions for electronic structure theory and computational science, J. Phys.: Condens. Matter, 26, 213201, (2014)
[4] EigenExa EigenExa, , http://www.r-ccs.riken.jp/labs/lpnctrt/en/projects/eigenexa/.
[5] T. Yano, Y. Futamura and T. Sakurai, Multi-GPU scalable implementation of a contour-integral-based eigensolver for real symmetric dense generalized eigenvalue problems, in: Proc. 3PGCIC 2013, pp. 121-127, IEEE Computer Society, 2013.
[6] L. Du; Y. Futamura; T. Sakurai, Block conjugate gradient type methods for the approximation of bilinear form \(C^{H}A^{-1}B\), Comput. Math. Appl., 66, 2446-2455, (2014) · Zbl 1368.65050
[7] A. Kozhevnikov, A. G. Eguiluz and T. C. Schulthess, Toward first principles electronic structure simulations of excited states and strong correlations in nano- and materials science, in: Proc. SC’10, pp. 1-10, IEEE Computer Society, 2010.
[8] A. Imakura; L. Du; T. Sakurai, Error bounds of Rayleigh–Ritz type contour integral-based eigensolver for solving generalized eigenvalue problems, Numer. Algorithms, 71, 103-120, (2016) · Zbl 1333.65039
[9] Y. Futamura; H. Tadano; T . Sakurai, Parallel stochastic estimation method of eigenvalue distribution, JSIAM Letters, 2, 127-130, (2010) · Zbl 1271.65063
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