Lanczos diagonalization procedure

This diagonalization can be performed by explicit construction of the matrix Haf ) which is then diagonalized by standard methods when the basis set is not too large. For the case of large systems and/or large basis sets, we will prefer iterative techniques, like the Lanczos method [74,143-145], which avoid the explicit construction of the Kohn-Sham matrix it is sufficient in these methods to have a procedure to apply (successively) the Kohn-Sham matrix on vectors cf. Only vectors cf need then to be stored. 

The importance of the block Lanczos method for many-body GF calculations has recently been discussed and demonstrated. In the case of the one-particle GF it has been shown that the computational effort of the diagonalization can be substantially reduced using block Lanczos. The proposed procedure consists of a block Lanczos prediagonalization of the N + l)-particle block and a subsequent diagonalization of the resulting smaller secular matrices and quite naturally exploits the specific structure of the Dyson equation. 

---