caa a22 4500 46575483X CHVBK 20180323111844.0 cr unu---uuuuu 170327e19901201xx s 000 0 eng 10.1007/BF01170010 doi (NATIONALLICENCE)springer-10.1007/BF01170010 Živković T. Department of Chemistry, Texas A & M University at Catveston, 77533, Catveston, Texas, USA aut Solution of the perturbed eigenvalue equation by the low-rank perturbation method [Elektronische Daten] [T. Živković] In its simplest form, the low-rank perturbation (LRP) method solves the perturbed matrix eigenvalue equationsAΨ ≡ (B + V)Ψ =εΨ, whereA, B andV are nth-order Hermitian matrices, and where the eigenstates and the eigenvalues of the unperturbed matrixB are known. The method can be applied to arbitrary perturbations V, but it is numerically most efficient if the rank ρ ofV is "small”. A special case of low-rank perturbations are localized perturbations (e.g. replacement of one atom with another, creation and destruction of a chemical bond, local interaction of large molecules, etc.). In the case of local perturbations with a fixed localizability I, the operation count for the calculation of a single eigenvalue and/or a single eigenstate isO(l 2 n). In the more general case of a delocalized perturbation with a fixed rank p, the operation count for the derivation of all eigenvalues and/or all eigenstates is O(π 2 n 2). For largen, the performance of the LRP method is hence at least one order of magnitude better than the performance of other methods. The obtained numerical results demonstrate that the LRP method is numerically reliable, and that the performance of the method is in accord with predicted operation counts. J.C. Baltzer AG, Scientific Publishing Company, 1990 Journal of Mathematical Chemistry Kluwer Academic Publishers 4/1(1990-12-01), 143-153 0259-9791 4:1<143 1990 4 10910 https://doi.org/10.1007/BF01170010 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01170010 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Živković T. Department of Chemistry, Texas A & M University at Catveston, 77533, Catveston, Texas, USA aut NATIONALLICENCE 773 0- Journal of Mathematical Chemistry Kluwer Academic Publishers 4/1(1990-12-01), 143-153 0259-9791 4:1<143 1990 4 10910 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer