On the interplay between inner and outer Krylov spaces applied to large matrix diagonalization algorithms

Large-scale matrix diagonalization techniques are reviewed in the context of Lagrangian function optimization. Based in the effective Hamiltonian theory, the idea of separation of a general matrix-vector problem in inner and outer space components relative to a given model (or reference) space is introduced to improve the Lagrange-Newton-Raphson targeted diagonalization scheme (LNRd). A new effective Krylov space Lagrange-Newton-Raphson diagonalization (EKS-LNRd) algorithm is proposed and compared with the previous LNRd and Davidson methods and some test cases are shown and discussed.