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One more question about the "Note on Recursion Methods" Date: 2007/10/07 15:43 Name: Yang Xu   <yangxu@uiuc.edu> Dear Prof. Ozaki, Thank you very much. I really appreciate your answer. I just have one more question. It is really important for us. I am wondering if there is a mistake in Eq. (2.37) on page 40 of your notes, should the \hat{H} be \hat{H'} where H'=S^{-1}H ? To compute the |r_n) in Eq.(2.37), we need first explicitly compute H' by using H'=S^{-1}*H, right? Your timely reply will be highly appreciated!! Best regards, Yang Xu

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Re: One more question about the "Note on Recursion Methods" ( No.1 ) Date: 2007/10/21 09:56 Name: T.Ozaki Hi, > I am wondering if there is a mistake in Eq. (2.37) on page 40 of your notes, > should the \hat{H} be \hat{H'} where H'=S^{-1}H ? It is correct as the symbolic notation, since the state in the left-hand side is written by the dual vector. But, your guess is right in practice since the original basis is used to represent the Hamiltonian. > To compute the |r_n) in Eq.(2.37), we need first explicitly > compute H' by using H'=S^{-1}*H, right? Instead, the following second step calculation can reduce the computational time. (i) (V| = (Un|S^{-1} (ii) (V|H But, as the recursion level is comparable to the matrix size of original Hamiltonian, they become comparable each other with respect to computational time. Regards, TO

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