This work focuses on the downlink and uplink of large-scale single-cell MU-MIMO systems in which the base station (BS) endowed with $M$ antennas communicates with $K$ single-antenna user equipments (UEs). Particularly, we aim at reducing the complexity of the linear precoder and receiver that maximize the minimum signal-to-interference-plus-noise ratio subject to a given power constraint. To this end, we consider the asymptotic regime in which $M$ and $K$ grow large with a given ratio. Tools from random matrix theory (RMT) are then used to compute, in closed form, accurate approximations for the parameters of the optimal precoder and receiver, when imperfect channel state information (modeled by the generic Gauss-Markov formulation form) is available at the BS. The asymptotic analysis allows us to derive the asymptotically optimal linear precoder and receiver that are characterized by a lower complexity (due to the dependence on the large scale components of the channel) and, possibly, by a better resilience to imperfect channel state information. However, the implementation of both is still challenging as it requires fast inversions of large matrices in every coherence period. To overcome this issue, we apply the truncated polynomial expansion (TPE) technique to the precoding and receiving vector of each UE and make use of RMT to determine the optimal weighting coefficients on a per-UE basis that asymptotically solve the max-min SINR problem. Numerical results are used to validate the asymptotic analysis in the finite system regime and to show that the proposed TPE transceivers efficiently mimic the optimal ones, while requiring much lower computational complexity.