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5
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79954421421
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note
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RPA can be more efficient than the direct solution especially when one is interested only to a frequency range where the excitations are well separated.
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7
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0003893794
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SIAM, Philadelphia
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Z. Bai, J. Demmel, J. Dongarra, A. Ruhe, H. van der Vorst (Eds.), Templates for the Solution of Algebraic Problems: A Practical Guide, SIAM, Philadelphia, 2000.
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Templates for the Solution of Algebraic Problems: A Practical Guide
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Bai, Z.1
Demmel, J.2
Dongarra, J.3
Ruhe, A.4
Vorst Der H.Van5
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15
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34247324846
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In principle it is possible to choose a different energy range, not necessarily containing the lowest energy, using the modification proposed by G. Grosso, L. Martinelli and G. Pastori Parravini
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Note that in the Lanczos approach the energy range includes always the lowest energies
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Note that in the Lanczos approach the energy range includes always the lowest energies. In principle it is possible to choose a different energy range, not necessarily containing the lowest energy, using the modification proposed by G. Grosso, L. Martinelli and G. Pastori Parravini, Phys. Rev. B 51 (1995) 13033-13038.
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(1995)
Phys. Rev. B
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0010610199
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H. Ehrenfest, F. Seitz, D. Turnbull (Eds.) Academic Press
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R. Haydock, in: H. Ehrenfest, F. Seitz, D. Turnbull (Eds.), Solid State Phys. 35 (1980) 215, Academic Press.
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(1980)
Solid State Phys
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Haydock, R.1
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18
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79954418986
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note
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In particular, at each iteration both the computational cost and the storage are increasing, since all the vectors in the basis are needed to determine the new one.
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19
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79954414582
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note
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In principle also the Hermitian algorithm can break down. In fact after many iterations, because of the numerical error, the vectors in the Lanczos basis may stop to be orthonormal.
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27
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79954420421
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note
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For real matrices, as in the case of TD-DFT for finite systems and local exchange-correlation functionals, the cost is reduced further, since one can construct before-hand the two matrix A = R + C and B = R - C, so that only a single matrix-vector multiplication is needed (giving another factor two). Moreover usually B reduces to a diagonal matrix, containing on the diagonal the energy differences of the particle-hole pairs. In this case the algorithm is equivalent to the one proposed by Casida, see Ref. [9].
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28
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0036827661
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X. Gonze, J.M. Beuken, R. Caracas, F. Detraux, M. Fuchs, G.M. Rignanese, L. Sindic, M. Verstraete, G. Zerah, and F. Jollet Comput. Mater. Sci. 25 2002 478
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Gonze, X.1
Beuken, J.M.2
Caracas, R.3
Detraux, F.4
Fuchs, M.5
Rignanese, G.M.6
Sindic, L.7
Verstraete, M.8
Zerah, G.9
Jollet, F.10
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20144367100
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X. Gonze, G.M. Rignanese, M. Verstraete, J.M. Beuken, Y. Pouillon, R. Caracas, F. Jollet, M. Torrent, G. Zerah, and M. Mikami Z. Kristallogr. 220 2005 558
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Z. Kristallogr.
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Gonze, X.1
Rignanese, G.M.2
Verstraete, M.3
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Pouillon, Y.5
Caracas, R.6
Jollet, F.7
Torrent, M.8
Zerah, G.9
Mikami, M.10
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70449533121
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X. Gonze, B. Amadon, P.M. Anglade, J.M. Beuken, F. Bottin, P. Boulanger, F. Bruneval, D. Caliste, R. Caracas, and M. Côté Comput. Phys. Commun. 180 2009 2582
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Caracas, R.9
Côté, M.10
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