Extremely large aperture array (ELAA) is a promising multiple-input multiple-output (MIMO) technique for next generation mobile networks. In this paper, we propose two novel approaches to accelerate the convergence of current iterative MIMO detectors in ELAA channels. Our approaches exploit the static components of the ELAA channel, which include line of sight (LoS) paths and deterministic non-LoS (NLoS) components due to channel hardening effects. This paper proposes novel convergence acceleration techniques for fast iterative ELAA-MIMO detection by leveraging the static channel component, including the LoS paths and deterministic NLoS components that arise due to channel hardening. Specifically, these static channel components are utilized in two ways: as preconditioning matrices for general iterative algorithms, and as initialization for quasi-Newton (QN) methods. Simulation results show that the proposed approaches converge significantly faster compared to current iterative MIMO detectors, especially under strong LoS conditions with high Rician K-factor. Furthermore, QN methods with the proposed initialization matrix consistently achieve the best convergence performance while maintaining low complexity.