Cross correlation functions C[sub nm](E) via Lanczos algorithms without diagonalization

Karlsson, Hans O.; Holmgren, Sverker
November 2002
Journal of Chemical Physics;11/22/2002, Vol. 117 Issue 20, p9116
Academic Journal
It is shown how the quasiminimal residual algorithm (QMR), based on the Lanczos algorithm, can be modified to compute cross-correlation functions C[SUBnm](E)=〈ψ[SUBn]¦(E-H)[SUP-1] ¦ ψ[SUBm]&gang;; without any diagonalization by recursively updating a small number of scalars. Only three Lanczos vectors need to be stored. Several left-hand side vectors 〈ψ[SUBn]¦ and multiple shifts E can be considered simultaneously. The new method is termed the quasiminimal recursive residue generation method (QM-RRGM) and is applied to the collinear H+H[SUB2] problem to illustrate its convergence behavior. The properties of two different formulations of the Lanczos algorithm, the usual three-term and a coupled two-term recursion, are also discussed. The QM-RRGM exhibits smooth convergence behavior, and it is shown that the stopping criteria used in the QMR algorithm can also be used for computing correlation functions.


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