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This is a question about numerical analysis used particularly in the computational condensed matter or anywhere where one needs to DIAGONALIZE GIGANTIC DENSE HERMITIAN MATRICES.

In order to diagonalize dense Hermitian matrices size of 25k-by-25k and more (e.g. 1e6-by-1e6) it is not enough to use canned routines like zheevx() in LAPACK. It's way too slow. One needs new state of the art routines like RMM-DIIS (Residual Minimisation-Direct Inversion in Iterative Subspace) from Wood, Zunger "A New Method for Diagonalising Large Matrices" [J.Phys.A - Mathematical and General, 18, 1343 (1985)]. Since, I have never written eigensolver before, can anyone with experience give an advice what I need to learn to do progam RMM-DIIS quickly. E.g. to give a list of methods and concepts, with book/chapters. Thanks.

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# Diagonalization of Gigantic Dense Hermitian Matrices

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