This paper considers large multiple-input multiple-output (MIMO) communication systems with linear precoding and linear minimum mean-squared error (LMMSE) equalization based on the iterative conjugate gradient (CG) algorithm. Convergence of the CG algorithm is fast when the eigenvalues of the received signal's covariance matrix are clustered, suggesting that mean-squared error and receiver complexity can be managed with judicious precoder design. In order to accelerate convergence of an iterative CG receiver, we incorporate constraints on two measures of eigenvalue clustering into the precoder design. Closed-form solutions to the optimal precoders are derived using majorization theory and convex optimization techniques. We show that if there are constraints on receiver complexity, the proposed precoders can improve performance for large MIMO systems operating over slowly time-varying fading channels.